The total amount in the acount in 5 years is approximately $13,321.76.
What is the accrued amount in the account in 5 years?The formula accrued amount in a compounded interest is expressed as;
[tex]A = P( 1 + \frac{r}{n} )^{n*t}[/tex]
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given that:
Principal P = $10,000Compounded monthly n = 12Time t = 5 yearsInterest rate r = 5 3/4% = 5.75%Accrued amount A = ?First, convert R as a percent to r as a decimal
r = R/100
r = 5.75/100
r = 0.0575
Plug the given values into the above formula and solve for A.
[tex]A = P( 1 + \frac{r}{n} )^{n*t}\\\\A = 10000( 1 + \frac{0.0575}{12} )^{(12*5)}\\[/tex]
A = $13,321.76
Therefore, the accrued amount is $13,321.76.
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P(RI-T) = 0.25, P(-R|T) = 0.2, P(T) = 0.1
What is P(R)?
O 0.245
O insufficient information
O 0.1060
O 0.305
Answer:
We can use Bayes' theorem to calculate P(R), which states that the probability of an event A given event B is equal to the probability of B given A multiplied by the probability of A, divided by the probability of B:
P(R|T) = P(T|R) * P(R) / P(T)
We can rearrange this equation to solve for P(R):
P(R) = P(R|T) * P(T) / P(T|R)
We are given that P(RI-T) = 0.25, which can be written as:
P(R∩T) = P(R|T) * P(T) = 0.25
We are also given that P(-R|T) = 0.2, which can be written as:
P(-R∩T) = P(-R|T) * P(T) = 0.2 * 0.1 = 0.02
We can use the law of total probability to find P(T|R):
P(T|R) = P(RI-T) / P(R) = 0.25 / P(R)
We can substitute these values into the equation for P(R) to get:
P(R) = P(R|T) * P(T) / P(T|R)
= 0.25 / [P(T|R) * P(T) + P(-R|T) * P(T)]
= 0.25 / [0.25 + 0.02]
= 0.1060
Therefore, the answer is option C: 0.1060.
1. A survey conducted by a national research center asked a random sample of 920
teenagers in the United States how often they use a video streaming service.
From the sample, 59% answered that they use a video streaming service every day.
a. Construct and interpret a 95% confidence interval for the proportion of all
teenagers in the United States who would respond that they use a video
streaming service every day.
b. Based on the confidence interval in part (a), do the sample data provide
convincing statistical evidence that the proportion of all teenagers in the United
States who would respond that they use a video streaming service every day is
not 0.5? Justify your answer.
Mean Standard Deviation Sample Size
Standard care 0.57 0.26 56
New treatment 0.69 0.27 56
2. Patients experiencing symptoms of a heart attack are routinely transported to a
hospital in an ambulance. In a study of a new treatment thought to reduce damage to
the heart, patients experiencing symptoms of a heart attack were randomly assigned to
one of two groups. During transportation to the hospital, patients in one group received
standard care, and patients in the other group received the new treatment consisting of
standard care and the application of a blood pressure cuff.
The response variable measured for each patient was a number between 0 and 1,
referred to as the myocardial salvage index (MSI). A higher MSI value indicates a more
positive outcome for the patient. Summary statistics for the MSI responses of the two
groups are shown in the table.
Do the data provide convincing statistical evidence that the new treatment results in a
higher mean MSI value than does the standard care among people similar to the
patients in the study?
Since the calculated t-value is greater than the critical t-value, we reject the null hypothesis, concluding that there's convincing evidence that the new treatment results in a higher mean MSI value than standard care.
How to solvea. The 95% confidence interval for the proportion of teenagers using video streaming services daily is (0.5579, 0.6221). This means we're 95% confident that 55.79% to 62.21% of US teenagers use such services daily.
b. The results demonstrate that the proportion is not 0.5 because the full confidence interval is higher than 0.5.2. We obtain a t-value of roughly 2.51 with 108.52 degrees of freedom using a two-sample t-test.
At a significance level of 0.05, the critical t-value for a one-tailed test is approximately 1.66.
Since the calculated t-value is greater than the critical t-value, we reject the null hypothesis, concluding that there's convincing evidence that the new treatment results in a higher mean MSI value than standard care.
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Harvey’s pizzeria has three pizza sizes he wants to work out the outside measurement (circumference) of each size to work out how much cheese he will need for a stuff crust.
Match the correct circumference of each pizza using the diameter given.
Small –
Medium-
Large-
The circumference of the small pizza is approximately 47.1 cm, the circumference of the medium pizza is approximately 69.1 cm, and the circumference of the large pizza is approximately 94.2 cm.
The diameter is the distance across the widest part of a circle. To find the circumference of a circle, we use the formula C = πd, where C is the circumference, π is a mathematical constant (approximated as 3.14), and d is the diameter of the circle. Therefore, to find the circumference of each pizza size, we can simply plug in the given diameter into this formula.
For the small pizza with a diameter of 15 cm, the circumference can be calculated as follows:
C = πd
C = 3.14 x 15
C ≈ 47.1 cm
For the medium pizza with a diameter of 22 cm, the circumference can be calculated as follows:
C = πd
C = 3.14 x 22
C ≈ 69.1 cm
For the large pizza with a diameter of 30 cm, the circumference can be calculated as follows:
C = πd
C = 3.14 x 30
C ≈ 94.2 cm
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Find to value of a if you knew the perimeter was 250 inches long
Answer:
To find the value of "a" when you know the perimeter of a shape, you need to know the specific shape you're referring to. Please provide more information about the shape in question, such as whether it's a rectangle, triangle, or another geometric figure. Additionally, if you have any specific measurements or relationships between the sides of the shape, please provide them as well.
please help me for 50 points!!
simplify: -3 √84x^3
A. -6x√21x
B. -6√21
C. 6x√21x
Answer:
C
Step-by-step explanation:
the prime factorization of 84 is 2 x2 x 3 x 7
I can rewrite the problem
-3[tex]\sqrt{84x^{3} }[/tex]
-3[tex]\sqrt{(2)(2)(3)(7)xxx}[/tex] pull out the pairs
-3(2)x[tex]\sqrt{(3)(7)x}[/tex]
-6x[tex]\sqrt{21x}[/tex]
Helping in the name of Jesus.
Transactions on Furnell's credit card are shown for the month of June. The interest rate is 1.4% per month.
June 1 Balance $352.12
June 4 Sears $331.89
June 8 eBay $81.58
June 15 Outback $30
June 18 Payment $200
Find the average daily balance $
184.89
Find the interest for the month $
Find the balance for the following month $
The interest for the month is: $2.59
The balance for the month is: $598.18.
We have the information from the question is:
The interest rate is 1.4% per month.
June 1 Balance $352.12
June 4 Sears $331.89
June 8 eBay $81.58
June 15 Outback $30
June 18 Payment $200
Now, According to the question:
The average daily balance for June is $184.89.
To calculate the interest for the month,
Multiply the average daily balance by the interest rate:
$184.89 × 1.4% = $2.59.
To find the balance for the month :
Add the initial balance, transactions, and interest, then subtract the payment:
$352.12 + $331.89 + $81.58 + $30 + $2.59 - $200 = $598.18.
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use synthetic division
PLEASE HELP!!
The quotient using a synthetic method of division is 8x² + 15x + 7/8 and the remainder is 71/64
How to evaluate the quotient using a synthetic methodThe quotient expression is given as
(8x³ + 14x² - 2x + 1) divided by x - 1/8
Using a synthetic method of quotient, we have the following set up
1/8 | 8 14 -2 1
|__________
Bring down the first coefficient, which is 8:
1/8 | 8 14 -2 1
|__________
8
Multiply 8 by 1/8 to get 1, and write it below the next coefficient and repeat the process
1/8 | 8 14 -2 1
|_____1_15/8__7/64_
8 15 7/8 71/64
So, the quotient is 8x² + 15x + 7/8 and the remainder is 71/64
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A gas station sells regular gas for $2.20 per gallon and premium gas for $2.75 a gallon. At the end of a business day 340 gallons of gas had been sold, and receipts totaled $803. How many gallons of each type of gas had been sold?
Using a system of equations, the quantities of each type of gas sold by the gas station for the business day are as follows:
Regular Gas = 240 gallonsPremium Gas = 100 gallons.What is a system of equations?A system of equations refers to two or more equations solved concurrently.
A system of equations is also known as simultaneous equations because they can be solved at the same time.
Regular Premium
Price per gallon $2.20 $2.75
Total number of gallons of gas sold = 340
The total receipts for the 340 gallons = $803.
Let the number of gallons of the regular gas = x
Let the number of gallons of the premium gas = y
Equations:x + y = 340 ...Equation 1
2.2x + 2.75y = 803 ...Equation 2
Multiply Equation 1 by 2.2:
2.2x + 2.2y = 748 ...Equation 3
Subtract Equation 3 from Equation 2:
2.2x + 2.75y = 803
-
2.2x + 2.2y = 748
0.55y = 55
y = 100
x = 240 (340 - 100)
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The graph shows the area in square feet Sally has left to paint. The equation A=392-14x gives the square feet Lisa has left to paint as a function of time in minutes. Which statements are true?
The statements that are true include the following:
B. Lisa paints more square feet per minute than Sally.
C. Lisa will finish painting before Sally.
D. After 10 minutes of painting Sally will have less to paint than Lisa.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (0 - 360)/(30 - 0)
Slope (m) = -360/30
Slope (m) = -12
At data point (0, 360) and a slope of -12, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 360 = -12(x - 0)
y = -12x + 360
A = 360 - 12x
For Sally, the time to finish;
360 = 12x
x = 360/12 = 30 min.
For Lisa, the time to finish;
392 = 14x
x = 392/14 = 28 min (Lisa will finish painting before Sally)
For Sally, when x = 10;
A = 360 - 12(10)
A = 240 sq. feet.
For Lisa, when x = 10;
A = 392 - 14(10)
A = 252 sq. feet.
For Sally, when x = 20;
A = 360 - 12(20)
A = 120 sq. feet.
For Lisa, when x = 20;
A = 392 - 14(20)
A = 112 sq. feet.
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Simplify using law of exponents. (3^4)^8
Step-by-step explanation:
[tex] {( ({3})^{4} })^{8} \\ = {3}^{32} [/tex]
aleks math please answer
The slope of the lines
Line 1 = -5/2
Line 2 = -5/4
Line 3 = -5/4
Line 1 and 2 are neither
Line 1 and 3 are neither
Line 2 and 3 are parallel
What is slope?Slope can be defined as the degree of steepness of a line.
The formula for calculating the slope of a line is expressed as;
Slope, m = y₂ - y₁/x₂ - x₁
Given that the line coordinates are;
(x₁, y₁)(x₂ , y₂)
For Line 1, we have;
(0, 7)(8 , -3)
Substitute the values, we get;
Slope, m = (-3 - 7)/(8 - 0)
subtract the values
Slope, m = -10/8 = -5/2
For line 2
(8, -8)(4, -3)
Substitute the values
Slope, m = -3 -(-8)/4 - 8
Slope, m = -5/-4 = 5/4
For Line 3
(-4, 3)(4, -7)
Substitute the values
Slope, m = -7 - (3)/4 -(-4)
Slope, m = -10/8 = -5/4
Note that, lines with the same slope are parallel and if the slope of one line is the negative reciprocal of the second line, then they are perpendicular.
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14. The distance between (x, 2) and (0, 6) is 5 units. Use the Distance Formula to determine
the value of x. Show all your work.
Answer:
The value of x is 3.
Step-by-step explanation:
The Distance Formula is:
d = √[(x2 - x1)² + (y2 - y1)²]
Using the given points, we have:
d = √[(0 - x)² + (6 - 2)²]
Simplifying inside the square root gives:
d = √[x² + 16]
We know that the distance between (x, 2) and (0, 6) is 5 units, so we can set up the equation:
5 = √[x² + 16]
Squaring both sides gives:
25 = x² + 16
Subtracting 16 from both sides gives:
9 = x²
Taking the square root of both sides gives:
x = ±3
Since we are looking for the value of x, we choose the positive solution:
x = 3
Therefore, the value of x is 3.
On Monday Harriet ate 1/4 of a 8 slice of pizza on Tuesday she ate 1/2 of the same pizza what fraction of The Whole Pizza did she eat
Harriet ate a total of 3/4 of the total pizza
Given data ,
On Monday Harriet ate 1/4 of a 8 slice of pizza
And , on Tuesday she ate 1/2 of the same pizza
Now , If the pizza has 8 slices, then Harriet ate 1/4 of 8 slices on Monday, which is 2 slices.
On Tuesday, Harriet ate 1/2 of the same pizza, which is 4 slices.
So, in total, Harriet ate 2 + 4 = 6 slices of pizza
On simplifying the equation , we get
The whole pizza has 8 slices, so Harriet ate 6/8 of the pizza, which simplifies to 3/4.
Hence , Harriet ate 3/4 of the whole pizza
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A straw is placed inside a rectangular box that is g inches by 6 inches by 7 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form.
Answer:
The length of the straw will be 5.91607 inches long in radical form.
What is Length of diagonal in cuboid?
If a cuboid has length = l units, breadth = b units, and height = h units, then we can evaluate the length of the diagonal of a cuboid using the formula
As per the question the length of the straw is equal to length of the diagonal of Rectangular box.
l= 3 inch , b= 5 inch , h= 1 inch
Let us consider the length of the straw be 'x'.
As, Diagonal of Cuboid is,
X= 5.91607 (in radical form)
Step-by-step explanation:
Hence, the length of the straw will be 5.91607 inches.
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Compare each pair of expressions using >, <, or =.
.-32
. |-32|
5 -5
15
___|15|
. |5|_____|-5|
2-17
▾
2 ____ |-17|
. |-27|_____|-45|
.-27______-45
Comparing each pair of expressions using >, <, or = is given below:
15 > |___15| (because |___15| is equal to 15)2 - 17 < ▾ (because 2 - 17 equals -15, which is less than the square root symbol)-27 > -45 (because -27 is closer to zero than -45)'How to solve-32 < |-32| (because -32 is negative and |-32| is positive)
5 - 5 = 0 (because subtracting the same number results in zero)
15 > |___15| (because |___15| is equal to 15)
|5| = |___|-5|| (because both expressions are equal to 5)
2 - 17 < ▾ (because 2 - 17 equals -15, which is less than the square root symbol)
2 > |____|-17|| (because 2 is positive and |-17| is also positive)
|-27| > ||-45|| (because |-27| is 27 and ||-45|| is 45)
-27 > -45 (because -27 is closer to zero than -45)
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is 2^7 equal to 2x 7
Answer: No, 2^7 is not equal to 2x7.
2^7 means 2 raised to the power of 7, which is 2 multiplied by itself 7 times:
2^7 = 2 x 2 x 2 x 2 x 2 x 2 x 2 = 128
On the other hand, 2x7 means 2 multiplied by 7:
2x7 = 2 x 7 = 14
So 2^7 is not equal to 2x7.
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
See, 2 ^ 7 is 2 TO THE POWER OF 7, which is repeated multiplication.
2 x 7 is 2 MULTIPLIED BY 7
2 ^ 7 written out completely is:
2 * 2 * 2 * 2 * 2 * 2 * 2 = 128
See the repeated multiplication above?
2 x 7 is just 14.
See the difference!
14 is NOT equal to 128
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Write an inequality that matches the number line model. Then write
a situation that the inequality could represent.
25 is less than x
Given the circle below with secants
�
�
�
‾
KLM
and
�
�
�
‾
ONM
. If
�
�
=
13
,
�
�
=
12
LM=13,NM=12 and
�
�
KL is
3
3 less than
�
�
ON, find the length of
�
�
‾
ON
. Round to the nearest tenth if necessary.
The length of ON for the intersecting secants is derived to be equal to 14
What is the intersecting secant theoremThe intersecting secant theorem, also known as the secant-secant theorem, states that when two secant lines intersect outside a circle, the product of the length of one secant segment and its external segment is equal to the product of the length of the other secant segment and its external segment.
MK × KL = MO × MN
note that KL = (ON - 3) so;
[13 + (ON - 3)] × 13 = (12 + ON) × 12
13(10 + ON) = 144 + 12ON
130 + 13ON = 144 + 12ON
13ON - 12ON = 144 - 130 {collect like terms}
ON = 14
Therefore, the length of ON for the intersecting secants is derived to be equal to 14
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Math question sb please do ts giving branliest
Answer:
All lines are parallel
Step-by-step explanation:
Get each equation in Slope-Intercept form:
1. Divide both sides by 3: [tex]y=-\frac{4}{3}x+\frac{7}{3}[/tex]
2. No change
3. Subtract 8x and divide by 6 on both sides: [tex]y=-\frac{4}{3}x-\frac{2}{3}[/tex]
Notice:
a. All slopes are -4/3, AND
b. All y-intercepts are different
An airplane is heading north at an airspeed of 550 km/hr, but there is a wind blowing from the southwest at 40 km/hr.
The plane will end up flying
degrees off course
The plane's speed relative to the ground will be
km/hr
Answer: To end up due north, the pilot will need to fly the plane 3.382 degrees east of north.
Step-by-step explanation:
don't know how to explain got it form chegg
ASAP
A rectangular prism is shown in the image.
A rectangular prism with dimensions of 3 yards by 5 yards by 5 and one half yard.
What is the volume of the prism?
forty one and one fourth yd3
fifty six and one fourth yd3
eighty two and one half yd3
165 yd3
As a result, the prism's volume is given by V = lwh = 3 x 5 x 5.5 = 82.5 cubic yards. Thus, option C—eighty two and a half yards—is the correct response.
what is volume ?The quantity of room an object takes up in three dimensions is measured by its volume. It is frequently expressed in cubic units like cubic metres, cubic feet, and cubic centimetres. Mathematics formulas that are particular to the shape of the object can be used to calculate its volume, such as V = l w h for a rectangular shape or V = (4/3)r3 for a sphere.
given
V = lwh is the formula for calculating the volume of a rectangular prism, where l, w, and h stand for the prism's length, width, and height, respectively.
Here, the dimensions are 3 yards in length, 5 yards in breadth, and 5.5 yards in height.
As a result, the prism's volume is given by V = lwh = 3 x 5 x 5.5 = 82.5 cubic yards.
Thus, option C—eighty two and a half yards—is the correct response.
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please answer i need help!!!!!!!!!!!!!!
Answer: 29
Step-by-step explanation:
<F is 29 degrees because 180-58=122 and 180-122= 58, so then you divide 58 by 2 to get 29 for each x. The x's are each equal to 29.
Answer:
29 degrees
Step-by-step explanation:
The problem shows angle HGE as 58 degrees.
Segment HF is 180 degrees so we can subtract 58 from 180 to get 122 degrees for angle g
Now, the sum of all angles in a triangle is 180.
So, there are 3 angles in the triangle:
g(we know this is 122)
e
f
the graph denotes that the measures of angle e and f are the same because they are the same variable.
Lets subtract 122 from 180 to get 58.
So, angle e and f together combine to make 58 degrees.
But we also know that e and f have the same measure.
So, to find the measure of f, simply divide 58/2 to get 29 degrees.
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8.6×10 ^7 bacteria are measured to be in a dirt sample that weighs 1 1 gram. Use scientific notation to express the number of bacteria that would be in a sample weighing 19 grams.
scientific notation to express the number of bacteria that would be in a sample weighing 19 grams would be 1.634 ×[tex]10^9[/tex].
what is scientific notationWith scientific notation, one can express extremely big or extremely small values.
When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation. For instance, 650,000,000 can be represented as 6.5 108 in scientific notation.
The given number of bacteria in the dirt sample is 8.6 × [tex]10^7[/tex], and the weight of the sample is 1 gram. To find the number of bacteria in a sample weighing 19 grams, we can use the following proportion:
number of bacteria / weight of sample = constant
We can solve for the constant by using the given information:
8.6 ×[tex]10^7[/tex] / 1 gram = constant
constant = 8.6 × [tex]10^7[/tex]
Now we can use this constant to find the number of bacteria in a 19-gram sample:
number of bacteria / 19 grams = 8.6 × [tex]10^7[/tex]
number of bacteria = 8.6 ×[tex]10^7[/tex] × 19 grams
To express the answer in scientific notation, we can multiply the two numbers and adjust the exponent accordingly:
number of bacteria = 1.634 × [tex]10^9[/tex]
Therefore, the number of bacteria in a sample weighing 19 grams would be 1.634 ×[tex]10^9[/tex]
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Fully factorise 3h² + 12h
Answer: To factorize 3h² + 12h, we can first find the greatest common factor (GCF) of the two terms, which is 3h:
3h(h + 4)
This is the fully factorized form of 3h² + 12h.
PLEASE HELPPPPP MEHHHH
A composite figure is composed of a semicircle whose radius measures 5 inches added to a square whose side measures 10 inches. A point within the figure is randomly chosen.
What is the probability that the randomly selected point is in the semicircular region?
Enter your answer rounded to the nearest tenth in the box.
%
A pair of standard dice are rolled. Find the
probability of rolling a sum of 7 with these dice.
Answer:
6 out of 36 or 1 out of 6
Step-by-step explanation:
There are 36 possible ways two dice can roll, so the probability of the sum of seven is 6 out of 36, or 1/6.
[tex]\boxed{\sf 16.67\%}.[/tex]
Step-by-step explanation:1. Determine the total amount of different outcomes.So since we have a pair of dice, assuming they are standard 6 faced dices, the total amount of outcomes is given by just multiplying the number of faces or different numbers that the dices can present:
6 x 6 = 36 possible outcomes.
2. Determine the amout of outcomes that meet the requirement of adding up to 7.Now, here we need to count all the possible cases where the outcome of both dices will equal 7. And there are said cases:
1 + 6 = 7
Explanation. Here the first dice presented number 1 and the second presented number 6, adding up to 7.
Other cases that meet the requirement:
2 + 5 = 7
3 + 4 = 7
4 + 3 = 7
5 + 2 = 7
6 + 1 = 7
So the total amount of events that will meet the requirement is 6.
3. Find the probability.So if we have an event with 36 possible outcomes, and only 6 of those 36 outcomes will mean a success on the experiment. Then, to find the probability of those 6 events from happening all we need to do is divide the amount of events considered "success" which is the numbers adding up to 7 by the total amout of outcomes (36).
So, the probability of rolling a sum of 7 with 2 dices is:
[tex]\sf P(\dfrac{6}{36} )=\dfrac{1}{6} =\boxed{\sf 16.67\%}.[/tex]
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Mateo produces a street sign graphic on his computer that is 4 inches by 5 inches. He enlarges the graphic by a scale factor of 3 to print. Then Mateo enlarges the image by a scale factor of 4 before sending it to the machinist.
What are the dimensions of the sign? Write the smaller dimension first and the larger dimension second.
The dimensions of the sign are as follows, using an overall scale factor of 12 on the original graphic:
Smaller Dimensions = 12 inches by 15 inchesLarger Dimensions = 48 inches by 60 inches.What is the scale factor?The scale factor refers to the ratio of an original scale, object, or drawing to its model or final version.
The scale factor may enlarge or reduce the original dimensions.
The dimensions of the street sign graphic on computer = 4 inches by 5 inches
Scale factor of the graphic on print = 3
The first smaller dimensions:
4 x 3 inches and 5 x 3 inches
= 12 inches by 15 inches
The second larger dimensions:
Scale factor = 4
12 x 4 inches by 15 x 4 inches60 i
= 48 inches by 60 inches
Overall scale factor of the original graphic to the last model = 12 (3 x 4)
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Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g. A. g(-4) = -11 B. g(0) = 2 C. g(7) = -1 D. g(-13) = 20
Answer:
Based on the information given, we know that the domain of g is -20 ≤ x ≤ 5 and the range is -5 ≤ g(x) ≤ 45. We also know that g(0) = -2 and g(-9) = 6.
A. g(-4) = -11: This statement could be true or false, as there is not enough information to determine its validity.
B. g(0) = 2: This statement is false, since we know that g(0) = -2.
C. g(7) = -1: This statement could be true or false, as there is not enough information to determine its validity.
D. g(-13) = 20: This statement is false, since -13 is outside the domain of g (-20 ≤ x ≤ 5).
Step-by-step explanation:Therefore, the statement that could be true for g is A. g(-4) = -11 or C. g(7) = -1.
Find the LCD of the given rational equation
The LCD of the rational equation above is 4(x + 7)(x - 7).
What is the explanation for the above response?To find the LCD (Least Common Denominator) of the given rational equation, we need to factor the denominators of each fraction and then take the product of the highest powers of each factor.
The first denominator, x^2 - 49, can be factored using the difference of squares formula:
x^2 - 49 = (x + 7)(x - 7)
The second denominator, 4x + 28, can be factored by factoring out the greatest common factor:
4x + 28 = 4(x + 7)
Therefore, the LCD is the product of the highest powers of each factor, which is:
LCD = 4(x + 7)(x - 7)
So we need to multiply each term in the equation by an appropriate form of 1 so that the denominators of all the fractions become the LCD, 4(x + 7)(x - 7).
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The hypotenuse of an isosceles right triangle is 13 centimeters longer than either of its legs. Find the exact length of
each side. (Hint: An isosceles right triangle is a right triangle whose legs are the same length.)
The length of one leg is
the length of the other leg is
(Simplify your answers. Type exact answers, using radicals as needed.)
and the length of the hypotenuse is
The length of the other legs of the isosceles right triangle is 13 + 13√2 centimetres.
How to find the sides of a right triangle?The hypotenuse of an isosceles right triangle is 13 centimetres longer than either of its legs.
An isosceles right triangle is a right triangle whose legs are the same length. The sides of a right triangle can be found using Pythagoras's theorem.
Therefore,
let
y = other legs
Therefore,
(x + 13)² = x² + x²
(x + 13)(x + 13) = 2x²
x² + 13x + 13x + 169 = 2x²
x² - 26x - 169 = 0
Therefore, using the quadratic formula,
[tex]\frac{-b+\sqrt{b^{2} - 4ac } }{2a}[/tex]
where
a = 1b = -26c = -169x = 13 ± 13√2
Therefore, we can only use positive values
x = 13 + 13√2
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