a)she need 3.68 negative point , The new APR for Moira will be 3.25% + (3.68 x 0.135%) = 3.7452% because each negative point raises the APR by 0.135%.and the breakeven time for Moira's loan is 10 months
What is Breakeven time?Breakeven time refers to the amount of time it takes for the savings from a particular action to equal the costs associated with that action. It is the point at which the benefits and costs are equal, and after which the benefits will begin to exceed the costs.
According to given informationa. Moira has to buy 14,000/380,000 = 0.0368 or 3.68% in negative points to offset $14,000 in closing fees. The closing expenses are reduced by 1% of the principle for every negative point, therefore Moira has to buy 3.68/1 = 3.68 negative points.
b. The new APR for Moira will be 3.25% + (3.68 x 0.135%) = 3.7452% because each negative point raises the APR by 0.135%.
c.When the savings from buying the negative points equal the additional interest paid because of the higher APR, that is the breakeven point for Moira's loan. 3.68 x 380,000 x 1% = $14,040 is the savings from buying 3.68 negative points. The difference between the interest paid at the original APR of 3.25% and the interest paid at the new APR of 3.7452% represents the additional interest paid as a result of the higher APR. A 10-year, $380,000 mortgage at 3.25% would have a monthly payment of $3,680.97 according to an online mortgage calculator. During a period of ten years, interest payments total $73,276.23. A 10-year, $380,000 mortgage at 3.7452% has a $3,918.23 monthly payment. Throughout a ten-year period, interest was paid a total of $88,668.83. The additional interest paid as a result of the higher APR equals $15,392.60 ($88,668.83 x $73,276.23). The breakeven point is therefore $14,040/$15,392.60 = 0.910 or roughly 10 months.
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If angle K measures 110°, angle J equals 36°, and k is 70 feet, then find j using the Law of Sines. Round your answer to the nearest tenth.
Answer:
43.8 feet
Step-by-step explanation:
In a triangle with angle K = 110°, J = 36°, and k = 70 feet, you want the measure of side j using the law of sines.
Law of sinesThe law of sines tells you side lengths in a triangle are proportional to the sine of the opposite angle. This means ...
j/sin(J) = k/sin(K)
j = k·sin(J)/sin(K) = (70 ft)·sin(36°)/sin(110°)
j ≈ 43.8 ft
The length of side j is about 43.8 feet.
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QUICK I’LL MARK YOU BRAINLIEST!! HELP ME FILL OUT THE SCRAMBLE WORD ON TOP!
Answer:
it can be rewritten as a percent
Step-by-step explanation:
nine bottles of equal capacity of 4.5 litters of water. how much does x bottles hold
6 bottles would hold 3 liters of water.
In general, the total capacity of x bottles would be 0.5x liters, where x represents the number of bottles.
If nine bottles have a total capacity of 4.5 liters, we can determine the capacity of each bottle by dividing the total capacity by the number of bottles.
In this case, we have:
Capacity per bottle = Total capacity / Number of bottles
= 4.5 liters / 9 bottles
= 0.5 liters per bottle.
Now, if we want to find out how much x bottles would hold, we can simply multiply the capacity per bottle by the number of bottles (x). Therefore, the formula to calculate the total capacity of x bottles would be:
Total capacity of * bottles = Capacity per bottle * Number of bottles
= 0.5 liters per bottle * x bottles
= 0.5x liters.
So, x bottles would hold 0.5x liters of water.
For example, if we wanted to find out how much 6 bottles would hold, we could substitute x with 6 in the formula:
Total capacity of 6 bottles = 0.5 * 6 liters
= 3 liters.
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Collect data on the OBSERVATION table in ANNEXURE A to record 30 days of the minimum and maximum temperature in your community. Arrange the maximum temperature of the 30 days in ascending order to summarize the data. Determine the mean, mode, median, and range. Use the maximum temperature data and draw for each section a frequency table with appropriate intervals in ANNEXTURE B Display or represent the data from the frequency table on a pie chart in ANNEXTURE B. First, calculate the size of the angles for the pie chart. Example: Intervals between 20-30 are 5. Therefore the proportion of the Segment: 11 [360° = 72° Show all your calculations. 11 Which data collection best describe the maximum and why?
Answer:
I do not have access to Annexure A and Annexure B, so I cannot collect the data, draw the frequency table or pie chart, or answer the last question. However, I can provide a general explanation of how to calculate the mean, mode, median, and range from a set of data.
To find the mean (average) of a set of data, add up all the values in the set and divide by the number of values. For example, if the maximum temperatures of the 30 days are:
25, 28, 29, 27, 26, 30, 31, 32, 29, 27, 26, 24, 23, 25, 28, 30, 32, 33, 34, 31, 29, 28, 27, 26, 25, 24, 23, 21, 20, 22
The sum of the values is:
25 + 28 + 29 + 27 + 26 + 30 + 31 + 32 + 29 + 27 + 26 + 24 + 23 + 25 + 28 + 30 + 32 + 33 + 34 + 31 + 29 + 28 + 27 + 26 + 25 + 24 + 23 + 21 + 20 + 22 = 813
Dividing by the number of values (30), we get:
Mean = 813/30 = 27.1
To find the mode of a set of data, identify the value that occurs most frequently. In this example, there are two values that occur most frequently, 27 and 29, so the data has two modes.
To find the median of a set of data, arrange the values in order from smallest to largest and find the middle value. If there are an even number of values, take the mean of the two middle values. In this example, the values in ascending order are:
20, 21, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 27, 28, 28, 29, 29, 29, 30, 30, 31, 31, 32, 32, 33, 34
There are 30 values, so the median is the 15th value, which is 28.
To find the range of a set of data, subtract the smallest value from the largest value. In this example, the smallest value is 20 and the largest value is 34, so the range is:
Range = 34 - 20 = 14
To create a frequency table for the maximum temperature data, we need to group the data into intervals and count the number of values that fall into each interval. For example, we could use the following intervals:
20-24, 25-29, 30-34
The frequency table would look like this:
Interval | Frequency
20-24 | 4
25-29 | 18
30-34 | 8
To calculate the size of the angles for the pie chart, we need to find the total frequency (30) and divide 360° by the total frequency to get the proportion of each interval in degrees. For example, for the interval 25-29:
Proportion = Frequency/Total frequency = 18/30 = 0.6
Angle = Proportion * 360° = 0.6 * 360° = 216°
We can repeat this calculation for each interval to obtain the angles for the pie chart.
In terms of the last question, it is not clear what is meant by "which data collection best describe the maximum and why?". If you could provide more context or clarification, I would be happy to try to help.
find the sum
-11 +3 + (-6)
Answer: -14
Step-by-step explanation:
Break up the question.
(-11 + 3) + (-6)
V V
(-9) (-14)
-11 + 3 = -9
-9 + (-6) = -14
Answer:
The answer is -14
Step-by-step explanation:
-11+3+(-6)
= -11+3-6
= -14
Find ||v-w||, if v = 5i - 2j and w = - 4i + 3j.
A motorist travels 228 kilometers in 6 hours. At that rate, how long will it take him to travel and additional 247 kilometers?
Answer:
The motorist's rate is:
rate = distance / time
where distance is measured in kilometers and time is measured in hours.
We are given that the motorist travels 228 kilometers in 6 hours, so we can use this information to find the rate:
rate = distance / time = 228 km / 6 hours = 38 km/hour
To find how long it will take the motorist to travel an additional 247 kilometers at this rate, we can use the same formula and solve for time:
time = distance / rate = 247 km / 38 km/hour ≈ 6.5 hours
Therefore, it will take the motorist approximately 6.5 hours to travel an additional 247 kilometers at the same rate of 38 km/hour.
how many batches of tires does the company have to manufacture and sell to have a profit of -$190,000?
Answer:
The profit equation is
Profit = Revenue - Cost
Let's assume the revenue per batch is $50,000 and the cost per batch is $35,000. Then the profit equation becomes:
Profit = ($50,000 x number of batches) - ($35,000 x number of batches)
Profit = $15,000 x number of batches
We want to find the number of batches that will give a profit of -$190,000, so we can set up the equation:
-$190,000 = $15,000 x number of batches
Solving for the number of batches, we get:
number of batches = -$190,000 / $15,000
number of batches = -12.67
This indicates that the firm would have to produce and sell around 13 batches of tyres in order to make a -$190,000 profit. However, because you can't produce and sell a fraction of a batch, the corporation would have to sell at least 14 batches to make the needed profit.
in the game of Yahtzee, five (6-sided) dice are used. How many different outcomes are possible when rolling these 5 dice?
There are 7,776 different outcomes when rolling five 6-sided dice.
How do we find the outcome of rolling 5 6-sided dice?In the game of Yahtzee, the dice used has 6 sides. This means that each dice has 6 possible outcomes.
Dice 1 = 6outcomes Dice 2 = 6 outcomes dice 3 = 6outcomes
Dice 4 = 6outcomes dice 5 = 6outcomes
We multiply all the outcomes by the total number of the 6-sided dice will be used for the game, which is 5.
We can express it as follows
6 × 6 × 6 × 6 × 6
It can also be expressed as 6⁵, the power 5 being the number of times that 6 will be multiplied
= 7776
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Triangle D has been dilated to create triangle D′. Use the image to answer the question. image of a triangle labeled D with side lengths of 3.6, 4.8, 5.2 and a second triangle labeled D prime with side lengths of x, 1.2, 1.3 Determine the scale factor used. 4 3 one third one fourth
The scale factor used is Option B: One fourth.
What is scale factor?
The scale factor of a shape refers to the amount by which it is increased or shrunk. It is applied when a 2D shape, such as a circle, triangle, square, or rectangle, needs to be made larger.
To find the scale factor, we can compare any corresponding side lengths between the original triangle and the dilated triangle.
Let's choose the longest side of triangle D, which is 5.2, and compare it to the longest side of triangle D′, which is x.
We know that a dilation multiplies all corresponding side lengths by the same factor, so -
scale factor = length of corresponding side in D′ / length of corresponding side in D
scale factor = x / 5.2
We don't have enough information to find x directly, but we can use the fact that the other two corresponding side lengths are 1.2 and 1.3.
Since the side lengths of triangle D were scaled by the same factor, we can set up the following equation -
1.2 / 3.6 = 1.3 / 4.8 = x / 5.2
Simplifying the equation -
0.3333... = 0.2708... = x / 5.2
x = 5.2 × 0.2708...
x ≈ 1.41
Now we can find the scale factor -
scale factor = x / 5.2 ≈ 1.41 / 5.2 ≈ 0.271
Therefore, the scale factor used was approximately 0.271.
Answer: One fourth.
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Answer:
1/4
Step-by-step explanation:
The before that answered first was correct! I also took the quiz so you guys dont have to!
what is the area of a circle with the diameter of 22 in with pi and a=Nr 2
Answer:
380.1327 square units
Step-by-step explanation:
A=pi*r^2
A=pi*121
A=380.1327
Mr burns built a wooden platform for the drama club at the school where he teaches the shape below represents the dimensions of this wooden platform picture is not to scale
The area of the wooden platform built by Mr. Burns for the drama club at the school is 288 square feet.
What are the dimensions of a rectangle?
A rectangle has two dimensions: a length and a width that are both perpendicular to it. An oval's or a triangle's interior likewise has two dimensions.
The area of a rectangle is determined by dividing its length by its width. Accordingly, the platform's area can be determined as follows:
Area = Length x Width
Area = 24 feet x 12 feet
Area = 288 square feet
Therefore, the area of the wooden platform built by Mr. Burns for the drama club at the school is 288 square feet.
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Find the product. Simplify the answer. 10 4 X 15 7
Answer:
Step-by-step explanation:
if this is decimals, I can totally do this. 10.4 x 15.7 = 163.28
look at the file attached
Write an equation in slope-intercept form for the graph shown.
Answer: y = 2x - 2
Step-by-step explanation:
you can see two points on the graph:
(0, -2) and (3, 3)
Using these to calculate the slope gives us:
(3+2)/(3-0) = 6/3 = 2
the y intercept is -2 as we can see
so the equation in slope intercept form is:
Write a whole number in each blank to show an expression that is equivalent to 12n-8
_•n+5n-_
Question about Convolution Sum
Let [tex]y[n] = x[n] * h[n][/tex], show that [tex]x[n - n_1] * h[n - n_2] = y[n - n_1 - n_2][/tex]
It is proved that [tex]x[n-n_1] × h[n-n_2] = y[n-n_1-n_2][/tex]
How to prove [tex]x[n-n_1] × h[n-n_2] = y[n-n_1-n_2][/tex]?
To prove that [tex]x[n-n_1] × h[n-n_2] = y[n-n_1-n_2][/tex] , we need to express the convolution sum of
[tex]x[n-n_1] \: and \: h[n-n_2][/tex], and then simplify it to obtain [tex]y[n-n_1-n_2][/tex]
Let's start by expressing the convolution sum of [tex]x[n-n_1] \: and \: h[n-n_2][/tex]
:[tex]x[n-n_1] ×h[n-n_2] = ∑ x[k-n_1] × h[n-n_2-k][/tex] where the summation is over all possible values of k.
Now, we can replace k with [tex]n - n_1 - m[/tex], which gives:
[tex]x[n-n_1] × h[n-n_2] = ∑ x[n-n_1-m] × h[n-n_2-n+n_1+m][/tex]
Next, we can rearrange the terms inside the summation to obtain:
[tex]x[n-n_1] × h[n-n_2] = ∑ x[n-m] × h[n-n_1-n_2+m][/tex]
Notice that the expression inside the summation is identical to the definition of y[n], so we can replace it with y[n] and simplify:
[tex]x[n-n_1] × h[n-n_2] = ∑ x[n-m] × h[n-n_1-n_2+m] = ∑ y[n-m] [/tex]
The last expression is the convolution sum of x[n] and h[n], which we know equals y[n]. Therefore:
[tex]x[n-n_1] × h[n-n_2] = y[n-n_1-n_2][/tex]
And we have proven that [tex]x[n-n_1] × h[n-n_2] = y[n-n_1-n_2][/tex]
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5. Find two equations of a circle if one of the end points of the diameter is at the origin and the radius is 3.
if one of the end points of the diameter is at the origin and the radius is 3 then the the equation of the circle in general form is:x² + y² - 3x = 0
What is Equation?An equation is a statement that shows the relationship between two or more variables using mathematical symbols. It expresses the equality or inequality between the values of the variables on either side of the equation.
According to the given information :
Since one of the endpoints of the diameter is at the origin, we know that the center of the circle is also at the origin. Let (x, y) be any point on the circle. Then, using the distance formula, we have:
√(x² + y²) = 3
Squaring both sides, we get:
x² + y² = 9
So, the equation of the circle in standard form is:
x² + y² - 9 = 0
Another way to write the equation of the circle is in general form, which is:
x² + y² + Dx + Ey + F = 0
where D, E, and F are constants. To find the values of D, E, and F, we substitute the coordinates of one of the points on the circle into the general form equation:
(0)² + (0)² + D(0) + E(0) + F = 0
F = 0
So, the equation of the circle in general form is:
x² + y² + Dx + Ey = 0
To find the values of D and E, we substitute the coordinates of another point on the circle into this equation. Let's use the point (3, 0) since we know it lies on the circle. Substituting these values, we get:
(3)²+ (0)² + D(3) + E(0) = 0
9 + 3D = 0
D = -3
Therefore, the equation of the circle in general form is:
x² + y² - 3x = 0
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Boris drove 360 miles in 5 hours.
At the same rate, how long would it take him to drive 936 miles?
Answer:
The answer is 13hours
Step-by-step explanation:
360miles------>5hours
936miles------->x hours
crossmultiply
x×360=936×5
360x=4680
divide both sides by 360
360x/360=4680/360
x=13hours
what does scaled version mean in this case its 3:5 scaled version but i just want to know what it means
A scaled version of any object is the object that has undergone a form of increment/enlargement or reduction has been made to the object. in the case of 3:5 scaled version, it tells you the ratio of increment or reduction that has happened to the object in comparison to the original object.
What is a scaled version using an example?In the height of an object has a 30cm height and perhaps a 12 cm width. Using a scaled version ratio provided which is 3:5. The scaled version f the object would be
3/5 x 30 = 18cm
3/5 x 12 = 7.2cm
A second example is if a rectangular room with dimensions 10 feet by 15 feet and you want to scaled version of 3:5, it becomes = 10 x (3/5) = 6 feet and 15 x (3/5) = 9 feet
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Will using name-brand microwave popcorn result in a greater
percentage of popped kernels than store- brand microwave popcorn?
To find out, Briana and Maggie randomly selected 10 bags of name-
brand microwave popcorn and 10 bags of store-brand microwave
popcorn. The chosen bags were arranged in random order. Then each
bag was popped for 3.5 minutes, and the percentage of popped kernels
was calculated. The data are displayed in the table.
Name brand 95
95 88 84 94 81 90 97 93 91 86
Store brand
91 89 82 82 77 78 84 86 86 90
Accordingly, utilising name-brand microwave popcorn rather than store-brand microwave popcorn is anticipated to yield a higher percentage of popped kernels based on the results of this study.
Test statistic: What is it?A test statistic is a numerical summary of a sample used in statistics to evaluate the strength of the evidence presented by the data in support of a certain conjecture about the population from which the sample was taken. A test statistic determines how many standard errors the observed data deviates from the predicted value by comparing it to what would be expected under the null hypothesis. To ascertain if an observed effect or difference between groups is the result of chance or if it is statistically significant, test statistics are employed in hypothesis testing.
Here,
We can compare the mean percentage of popped kernels between the two groups using a hypothesis test to see if using name-brand microwave popcorn yields a higher proportion of popped kernels than store-brand microwave popcorn.
Let μ1 be the mean percentage of popped kernels for name-brand microwave popcorn and μ2 be the mean percentage of popped kernels for store-brand microwave popcorn.
The null hypothesis states that there is no distinction between store-brand and name-brand microwave popcorn in terms of the mean percentage of popped kernels:
H0: μ1 - μ2 = 0
The alternate theory is that name-brand microwave popcorn has a mean percentage of popped kernels that is higher than that of store-brand microwave popcorn:
Ha: μ1 - μ2 > 0
This hypothesis can be examined using a two-sample t-test with unequal variances. For a one-tailed test with 18 degrees of freedom and a significance threshold of 0.05, the crucial t-value is 1.734.
Based on the information provided, we can determine that the sample mean percentage of popped kernels for name-brand microwave popcorn is 90.9% with a sample standard deviation of 5.09% and the sample mean percentage of popped kernels for store-brand microwave popcorn is 85.9% with a sample standard deviation of 4.67%.
We can calculate the test statistic as follows:
t = (x1 - x2 - 0) / √(s1²/n1 + s2²/n2)
t = (90.9 - 85.9) / √((5.09²/10) + (4.67²/10))
t = 2.26
We can reject the null hypothesis and come to the conclusion that there is enough evidence to support the claim that using name-brand microwave popcorn results in a greater percentage of popped kernels than store-brand microwave popcorn at the 0.05 level of significance because the calculated t-value (2.26) is greater than the critical t-value (1.734).
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A certain drug is made from only two ingredients: compound A and compound B. There are 3 milliliters of compound A used for every 5 milliliters of compound
B. If a chemist wants to make 728 milliliters of the drug, how many milliliters of compound A are needed?
? milliliters of compound A
In order to create 728 millilitres of the medication, 273 millilitres of component A are required.
What do you mean by compound?A compound in chemistry is a material comprised of two or more separate chemical elements mixed together in a certain proportion. Chemical connections that are challenging to break are created when the elements interact with one another.
Compound A:Compound B ratio in the medication is 3:5. In other words, there are 3 millilitres of compound A and 5 millilitres of compound B for every 3+5=8 millilitres of the medicine.
We may set up a percentage using the ratio of compound A to the total volume of the medicine to determine how much compound A is required to make 728 millilitres of the drug:
3 ml x 3 ml x 3 ml
-------- = ----------
728 ml total, 8 ml overall
If we cross-multiply, we obtain:
8(x) = 3(728)
To find x, we use the formula x = 3(728)/8 = 273
In order to create 728 millilitres of the medication, 273 millilitres of component A are required.
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273 milliliters of compound A are needed to make 728 milliliters of the drug.
What are proportions?
In mathematics, a proportion is a statement that two ratios are equal. It expresses the relationship between two or more quantities that are directly proportional to each other. A proportion can be represented as an equation of the form:
a/b = c/d
To determine the amount of compound A needed to make 728 milliliters of the drug, we need to use the given ratio of 3 milliliters of compound A to 5 milliliters of compound B.
Let's start by finding the ratio of compound A to the total amount of ingredients (A+B) in the drug:
3 : (3+5) or 3:8
This means that for every 8 milliliters of the drug, 3 milliliters of compound A are used.
To find out how many milliliters of compound A are needed for 728 milliliters of the drug, we can set up a proportion:
3/8 = x/728
where x represents the amount of compound A needed.
To solve for x, we can cross-multiply:
8x = 3*728
8x = 2184
x = 273
Therefore, 273 milliliters of compound A are needed to make 728 milliliters of the drug.
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Question 5 of 10
If your starting salary is $50,000 and you receive a 4% increase at the end of
every year, what is the total amount, in dollars, you will earn over the first 16
years that you work?
Round your answer to the nearest whole dollar, and express your answer
without using commas.
Answer here
Answer:
80000
Step-by-step explanation:
4% increase of 50000 is 2000 at the end of each year
so 2000*16=32000
50000+32000=82000
nearest whole dollar is 80000
Infuse 0.8 liters for 9 hours at a drop factor of 60 gtt/ ml. how many ml will be infused per hour
According to the question of drop factor, the answer is 53.3ml that will be infused per hour.
What is drop factor?Drop factor is a mathematical concept related to the concept of rate. It is a unitless coefficient used to adjust a given rate. Drop factor is commonly used to represent the rate of change in a linear equation, and can be used to calculate the rate at which a given value decreases over time. The drop factor is calculated by subtracting the previous value from the current value and dividing it by the change in time. This value can then be used to calculate the rate of change over time.
The calculation for the amount of ml that will be infused per hour is as follows:
Volume (L) x Drop Factor (gtt/ml) = Total Drops
0.8 L x 60 gtt/ml = 480 drops
Total Drops / Time (hours) = Drops/Hour
480 drops / 9 hours = 53.3 drops/hour
Since 1 drop is equal to 1 ml, this means 53.3 ml of fluid will be infused per hour.
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Drag equivalent fractions into the correct boxes.
2
4
2
3
6
8
2
6
4
8
3
4
1
3
4
6
The equivalent fractions when paired up would be:
2 / 4 - 4 / 8 2 / 3 - 4 / 6 6 / 8 - 3 / 4 2 / 6 - 1 / 3 How to find the equivalent fractions ?We must first simplify each fraction before categorizing them according to their simplified form in order to couple equivalent fractions. Since 2/4 and 4/8 may both be reduced to 1/2, they are equal.
The same is true of 2/3 which may be reduced to 4/6, they are both equivalent. 3/4 is the same as 6/8, they are equivalent.
Since 1/3 may be simplified to 2/6, they are equivalent.
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According to the information, the classification of the fractions would be: 3/4 = 6/8, 1/3 = 2/6, 4/6 = 2/3
How to classify the fractions in the correct option?To classify the fractions in the correct option box we can carry out two procedures. The first one is to simplify the fractions to identify which ones are equivalent to those in the boxes. On the other hand, we can do the divisions of the fractions and those that have the same results go in the same box. According to the above, the fractions are classified as follows:
3/4 = 6/81/3 = 2/64/6 = 2/3Note: This question is incomplete. Here is the complete information:
Attached image
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Need help asap pls and thx pic is attached
The value of x in the right triangle is 5.6 units.
How to find the side of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, the side length x of the right triangle can be found using trigonometric ratios as follows:
tan 48 = opposite / adjacent
where
opposite side = x
adjacent side = 5
Hence,
tan 48 = x / 5
cross multiply
x = 5 tan 48
x = 5 × 1.11061251483
x = 5.55306257415
Therefore,
x = 5.6 units
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a probability experiment consists of rolling a fair 8-sided die. Find the probability of the event below. rolling a 3
On a fair 8-sided die, the probability of rolling a 3 is 1/8, or 0.125, which is equivalent to 12.5% in percentage terms.
What is probability?The possibility or likelihood that an event will occur is measured by probability.
A number between 0 and 1, where 0 indicates that the occurrence is hypothetical and 1, meaning it is inevitable, is used to express it.
To put it another way, probability is the ratio of likely outcomes to real outcomes that pertain to a particular occurrence.
Every result (rolling any number from 1 to 8) is equally likely since the die is fair.
There are only two ways to roll a 3, and there are a total of eight outcomes.
As a result, the probability of rolling a 3 is:
P(rolling a 3) = 1/8
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Megan surveyed the 8th grade to find which school activities they attended last weekend. The results are shown in the two-way table.
The valid conclusions about the data being surveyed is Option A: Of the students who attended the basketball game, fewer than half of them also attended the school play.
What is a survey?
Questioning a group of people in a survey is one way to collect information from them. Surveys can be carried out using a variety of methods, including paper and pencil, online forms, the telephone, or in-person interviews.
A. Of the students who attended the basketball game, fewer than half of them also attended the school play. (True)
To calculate this, we need to divide the number of students who attended both the basketball game and the school play (55) by the total number of students who attended the basketball game (118).
55/118 = 0.466 = 46.6%, which is less than half.
B. More than half of the students who were surveyed attended the school play and did not attend the basketball game. (False)
To calculate this, we need to add up the number of students who attended the school play and did not attend the basketball game (63) and divide by the total number of students surveyed (221).
63/221 = 0.285 = 28.5%, which is less than half.
C. Students who attended the school play were more likely not to attend the basketball game. (False)
To calculate this, we need to compare the number of students who attended the school play and did not attend the basketball game (63) to the number of students who did not attend the school play and did not attend the basketball game (15).
63/78 = 0.808 = 80.8% and 15/78 = 0.192 = 19.2%. Since 80.8% is greater than 19.2%, we can conclude that students who attended the school play were more likely to attend the basketball game.
Therefore, valid conclusions is A.
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Can you please show your work
The value when x approaches to 0 the function approaches to 2.718.
What is the constant e?In many different mathematical situations, particularly in calculus and analysis, the special number e is used. Although its precise number is an infinite decimal with no pattern, it is roughly equal to 2.71828. The limit of the formula as n approaches infinity is the definition of the constant e. The letter e stands for this limit, which is real and equivalent to a particular number. In many branches of mathematics and science, including the study of exponential and logarithmic functions, the constant e is crucial. It can be used in physics, probability theory, and mathematics, among other things.
The given function is: [tex]\ lim (x \to 0) \frac{2^x - 1}{x}[/tex].
Substituting the value of x = 0.01 we have:
[tex]\ lim (x \to 0) \frac{2^{0.01} - 1}{0.01}\\[/tex]
f(x) = 2.704
Similarly substituting the values of x from the table we have:
x f(x)
0.01 2.704
0.001 2.718
0.0001 2.7182
-0.0001 2.7181
-0.001 2.716
-0.01 2.669
Hence, as the x approaches to 0 the function approaches to 2.718.
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Question 1-2
What is the value of a³ + b (6 + c), when a = 2, b = 3, and c = 4?
Answer:
[tex]\huge\boxed{\sf 38}[/tex]
Step-by-step explanation:
Given expression:= a³ + b (6 + c)
Put a = 2, b = 3 and c = 4
= (2)³ + 3 (6 + 4)
= 8 + 3(10)
= 8 + 30
= 38[tex]\rule[225]{225}{2}[/tex]
Answer:
Step-by-step explanation:
the requied answer is 38.
according to the question the value of a=2,b=3,c=4.
here,
to find the value of a³ + b (6 + c)we have to do it in steps:
step 1: solve the bracket (6+4) =10.
step 2: solve the value of a³ =8.
now put these values ,
=8+3(10)
=38.
Which inequality represents the graphed region in factored form?
y less-than-or-equal-to negative .25 (x + 12)(x minus 8)
y less-than-or-equal-to negative 4 (x minus 12)(x + 8)
y less-than-or-equal-to negative 4 (x + 12)(x minus 8)
y less-than-or-equal-to negative .25 (x minus 12)(x + 8)
The correct inequality that represents the graphed region in factored form is: option a.) [tex]y \leq -0.25 (x + 12)(x - 8)[/tex]
How to check if inequality represents the graphed region in factored form?[tex]y \leq -0.25 (x + 12)(x - 8)[/tex]: represents a region below or on the graph of the quadratic function with factors [tex](x + 12)(x - 8)[/tex], and the coefficient of y is -0.25.[tex]y \leq -4 (x - 12)(x + 8)[/tex]: represents a region below or on the graph of the quadratic function with factors[tex](x + 12)(x - 8)[/tex], and the coefficient of y is -4.[tex]y \leq -4 (x + 12)(x - 8)[/tex]: represents a region below or on the graph of the quadratic function with factors [tex](x + 12)(x - 8)[/tex], and the coefficient of y is -4.[tex]y\leq -0.25 (x - 12)(x + 8)[/tex]: represents a region below or on the graph of the quadratic function with factors[tex](x - 12)(x + 8)[/tex], and the coefficient of y is -0.25.Learn more about factored form here:
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