Answer:
17.8 in x 21.8 in
Step-by-step explanation:
Given w=width and l=length
w*l=390
l=w+4, therefore w*(w+4)=390
w^2+4w=390
w^2+4w-390=0
Quadratic equation, solve as such
w=-21.8 or 17.8
Solution can't be negative so w=17.8 in
l=w+4 so l=21.8
An orange is shot up into the air with a catapult. The function h given by
h(t) = 15 + 60t – 16t2 models the orange's height, in feet, 1 seconds after it was
launched.
Question 5 What is the initial speed at which the orange is shot in the air?
Answer:
Velocity = 59 feet/second
Step-by-step explanation:
h(t) = 15 + 60t – 16t2
Time t = 1 second
Let's substitute time into the equation to get the distance
h(t) = 15+60(1)-16(1)²
h(t) = 15 + 60 - 16
h(t) = 59 feet
Speed or velocity = distance/time
Distance = 59 feet
Time = 1 second
Velocity = 59/1
Velocity = 59 feet/s
How many solutions does the system have? y = -2x-4 \\\\ y = 3x+3
Answer:
The system has one solution.
Step-by-step explanation:
We have two equations:
y = -2x - 4
y = 3x + 3
Equalling them:
y = y
-2x - 4 = 3x + 3
5x = -7
[tex]x = -\frac{7}{5}[/tex]
And
[tex]y = 3x + 3 = 3(-\frac{7}{5}) + 3 = \frac{-21}{5} + 3 = \frac{-21}{5} + \frac{15}{5} = -\frac{6}{5}[/tex]
Replacing in the other equation we should get the same result.
[tex]y = -2x - 4 = -2(-\frac{7}{5}) - 4 = \frac{14}[5} - 4 = \frac{14}{4} - \frac{20}{5} = -\frac{6}{5}[/tex]
So the system has one solution.
Consider the relation S(x, y) : x is a brother or sister of y on the set, H, of living humans. (For the purposes of this problem, a sibling of a person means another person with the same two parents, so don’t consider half siblings.) Determine which of the three properties, reflexive, symmetric, transitive, hold for the relation S (explain your three answers). Is S an equivalence relation on H?
Answer:
- Not reflexive
- Symmetric
- Transitive
Step-by-step explanation:
- A person is not a sibling of himself so the relation is NOT reflexive
- If a person is a sibling of an other person, the other person is a sibling of the person. Therefore the relation is SYMMETRIC
- If a person A is a sibling of B, and a person B is a sibling of C then, person A is a sibling of person C. Therefore the relation is TRANSITIVE.
The relationship of variance and mean informs researchers about the spread of data. If a researcher calculates the mean abundance per unit area of a species, and then calculates the variance, the relationship between mean and variance will reflect the distribution pattern.
Which distribution pattern pictured below will have variance greater than the mean?
Answer:
The distribution pattern that will have variance greater than mean is one where the population of species is clustered and thus far from the mean abundance of species per unit area.
This distribution pattern can be found, using the POISSON distribution.
Step-by-step explanation:
Variance is a measure of dispersion while Mean is a measure of central tendency.
The mean is the average of all values (in this case, the abundance or concentration of species per unit area). It is the sum total of all values, divided by the number of values there are.
The variance of a given set of data, on the other hand, is a measure of the spread or distance or dispersal of the data from the mean. It measures the spread between each datum/value and the mean value.
The relationship between mean and variance surely reflects the pattern that the distribution will take. The kind of distribution pattern that will have a greater variance than mean is a Poisson distribution. Sample size is usually large here. Since the variance is greater than the mean, the population is a clustered or clumped distribution.
Identify the word form of this number: 139,204,539,912
One hundred thirty-nine billion, two hundred four million, five hundred thirty-nine thousand, nine hundred twelve.
Hope this helped!
find the equivalent expression using the same bases. (21 x15)9
Answer:
2835
Step-by-step explanation:
(21×15)9=
(315)9=
2835
Do the points shown represent additive inverses? Explain why or why not
Answer:
Yes additive inverse is two complete opposite numbers if added = 0
Answer:
additive
Step-by-step explanation:
Because the point is not past the postive live or below the negative.
What measures of the cylinder do 12 and 42 describe?
A cylinder with height of 42 millimeters and radius of 12 millimeters.
radius and diameter
radius and height
diameter and height
diameter and area of base
Answer: radius and height
Step-by-step explanation:
Radius is the distance between the center of the circle to its boundary.
Height is the length of the figure from top to bottom.
Given statement : A cylinder with height of 42 millimeters and radius of 12 millimeters.
That clearly means that the cylinder is having radius of 12 millimeters i.e. 12 is representing the measure of the radius of the cylinder.
And Similarly, 42 is representing the measure of the height of the cylinder.
Hence, the 2 and 42 describe the radius and height respectively of the cylinder.
Answer:
radius and height
Step-by-step explanation:
i just took the test edge 2020. rate me 5 stars!
Which of the following are true? If false, explain briefly.a) A P-value of 0.01 means that the null hypothesis is false.b) A P-value of 0.01 means that the null hypothesis has a 0.01 chance of being true.c) A P-value of 0.01 is evidence against the null hypothesis.d) A P-value of 0.01 means we should definitely reject the null hypothesis
Answer:
a) false
b) true
c) false
d) false
Step-by-step explanation:
a) p-value is compared with test statistic to either accept or ereject the null hypothesis. There is no fixed p-value to reject the null hypothesis
b) p-value tells us the probabiltiy of finding null hypothesis to be true
c) There is no fixed p-value for nullyfying the the null hypothesis
d) There is no fixed p-value to reject the null hypothesis
Write an integral for the area of the surface generated by revolving the curve y equals cosine (2 x )about the x-axis on negative StartFraction pi Over 5 EndFraction less than or equals x less than or equals StartFraction pi Over 5 EndFraction .
Answer:
The integral is
∫ˣ²ₓ₁ 2π cos 2x √[1 + 4 sin² 2x] dx
x₁ = (-π/5)
x₂ = (π/5)
And the area of the surface generated by revolving = 9.71 square units
Step-by-step explanation:
When a function y = f(x) is revolved about the x-axis, the formula for the area of the surface generated is given by
A = 2π ∫ˣ²ₓ₁ f(x) √[1 + (f'(x))²] dx
A = 2π ∫ˣ²ₓ₁ y √[1 + y'²] dx
For this question,
y = cos 2x
x₁ = (-π/5)
x₂ = (π/5)
y' = -2 sin 2x
1 + y'² = 1 + (-2 sin 2x)² = (1 + 4 sin² 2x)
So, the Area of the surface of revolution is
A = 2π ∫ˣ²ₓ₁ y √[1 + y'²] dx
= ∫ˣ²ₓ₁ 2πy √[1 + y'²] dx
Substituting these variables
A = ∫ˣ²ₓ₁ 2π cos 2x √[1 + 4 sin² 2x] dx
Let 2 sin 2x = t
4 cos 2x dx = dt
2 Cos 2x dx = (dt/2)
dx = (1/2cos 2x)(dt/2)
Since t = 2 sin 2x
when x = (-π/5), t = 2 sin (-2π/5) = -1.90
when x = (π/5), t = 2 sin (2π/5) = 1.90
A
= ∫¹•⁹⁰₋₁.₉₀ π (2 Cos 2x) √(1 + t²) (1/2cos 2x)(dt/2)
= ∫¹•⁹⁰₋₁.₉₀ (π/2) √(1 + t²) (dt)
= (π/2) ∫¹•⁹⁰₋₁.₉₀ √(1 + t²) (dt)
But note that
∫ √(a² + x²) dx
= (x/2) √(a² + x²) + (a²/2) In |x + √(a² + x²)| + c
where c is the constant of integration
So,
∫ √(1 + t²) dt
= (t/2) √(1 + t²) + (1/2) In |t + √(1 + t²)| + c
∫¹•⁹⁰₋₁.₉₀ √(1 + t²) (dt)
= [(t/2) √(1 + t²) + (1/2) In |t + √(1 + t²)|]¹•⁹⁰₋₁.₉₀
= [(1.90/2) √(1 + 1.90²)+ 0.5In |1.90+√(1 + 1.90²)|] - [(-1.9/2) √(1 + -1.9²) + (1/2) In |-1.9 + √(1 + -1.9²)|]
= [(0.95×2.147) + 0.5 In |1.90 + 2.147|] - [(-0.95×2.147) + 0.5 In |-1.90 + 2.147|]
= [2.04 + 0.5 In 4.047] - [-2.04 + 0.5 In 0.247]
= [2.04 + 0.70] - [-2.04 - 1.4]
= 2.74 - [-3.44]
= 2.74 + 3.44
= 6.18
Area = (π/2) ∫¹•⁹⁰₋₁.₉₀ √(1 + t²) (dt)
= (π/2) × 6.18
= 9.71 square units.
Hope this Helps!!!
∠BAD is bisected by . If m∠BAC = 2x - 5 and m∠CAD = 145, the value of x is:
Answer:
x = 75
Step-by-step explanation:
Assuming the angles are equal ( bisected means divided in half)
2x-5 = 145
Add 5 to each side
2x-5+5 = 145+5
2x = 150
Divide by 2
2x/150/2
x = 75
Answer:
x=75
Step-by-step explanation:
∠BAD is bisected by AC and measurement of BAC is equal to 2x - 5 and measurement of CAD is equal to 145. Since they are bisected, they are equal and the solution is shown below:
m ∠ BAC = m ∠ CAD
2x - 5 = 145 , transpose -5 to the opposite side such as:
2x = 145 + 5 , perform addition of 145 and 5
2x = 150
2x / 2 = 150 / 2 , divide both sides by 2
x = 75
The answer is 75 for the x value.
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
C. F(x) = 4x² + 1
Step-by-step explanation:
→The function F(x) shifted 1 unit upwards, meaning there needs to be a 1 being added to the function.
→In addition, the function F(x) has grown narrower, compared to the function G(x). This is from the absolute value of a number being greater than 1, which is being multiplied.
This means the correct answer should be "C. F(x) = 4x² + 1."
I need help this question is kinda confusing
Answer:
Geometric Sequence.
Step-by-step explanation:
Geometric sequence. If you take a close look at the graph, it never touches the x - axis. If you use division in a geometric sequence, you will get a very small number, but you will never touch the axis.
Anyone know how to solve this
Answer:
Y=1800+150x
Step-by-step explanation:
Answer:
4. Y = 150x + 1800
A battery with 20% percent of its full capacity is connected to a charger. Every minute that passes, an additional 5% percent of its capacity is charged. How do you graph this
Answer:
The relation between battery capacity and time is:
[tex]Y=0.05t+0.2[/tex]
The graph is attached.
Step-by-step explanation:
We will graph the charged capacity of the battery in function of time.
The rate of charge is constant, so we can conclude the relation is linear.
At time t=0, the battery capacity is at 0.2 (or 20%).
Every minute that passes, an additional 5% percent of its capacity is charged. So we can say that at t=1, the battery capacity is 0.2+0.05=0.25 (or 25%).
We can calculate the slope of the linear function as:
[tex]m=\dfrac{\Delta Y}{\Delta t}=\dfrac{0.05}{1}=0.05[/tex]
Then, the relation between battery capacity and time is:
[tex]Y=0.05t+0.2[/tex]
At a football game, a vender sold a combined total of 152 sodas and hot dogs. The number of sodas sold was three times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.
Answer:
38 hot dogs114 sodasStep-by-step explanation:
Sometimes problems of this nature are easily worked by considering groups of items. Here, it is convenient to consider a group as 1 hot dog and 3 sodas, so the number of sodas in the group is 3 times the number of hotdogs in the group.
Each group is 4 items, so 152/4 = 38 groups were sold.
In the 38 groups, there were 38 hot dogs and 3×38 = 114 sodas.
114 sodas and 38 hot dogs were sold.
Solve sin2x=-1/2 on the interval 0≤ angle≤360°
Answer:
x=135
Step-by-step explanation:
We know that sin(270) = -1/2
So 2x = 270
x = 135
Five people have just won a $100 prize, and are deciding how to divide the $100 up between them. Assume that whole dollars are used, not cents. Also, for example, giving $50 to first person and $10 to the second is different from vice versa. (a) How many ways are there to divide up the $100, such that each gets at least $10?
Answer:
give $20 to each person
Step-by-step explanation:
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
HELP PLEASE
Answer:
y=2/3x+1
Step-by-step explanation:
The slope is 2/3 and the y-intercept is 1.
Please answer this correctly
Answer: 207^2 + 9km^2 = 216km^2
Step-by-step explanation:
(my explanation is wrong)
All you want to do is break this figure up into rectangles and triangles.
I see 3 rectangles and 1 triangle.
Three Rectangles:
The bottom one has the dimension of 5 and 20. 5 x 20 = 100 km^2
The middle one has the dimensions of 5+4 and 7. 9 x 7 = 63 km^2
The top one has the dimensions of 4 and 11. 4 x 11 = 44 km^2
Add them all up to get 207km^2
One Triangle:
We can see at the bottom rectangle that the left side is 5 and the right side is 3 + x. X being our missing height of the triangle. The height equals 2.
The triangle now has the dimensions of 2 and 6. 2 x 6 = 12. Then divide by 2 to get 6 km^2
Answer:
216 km²
Step-by-step explanation:
To solve this, you have to divide the figure into different parts. I divided the parts up into four sections. I will work on the parts in numerical order.
1. At the top of the rectangle, it is marked 4 km. On the left side, it is marked 11 km. This is the length and width.
A = lw
A = 11 × 4
A = 44 km²
2. On the left side of this rectangle, it is marked 7 km. At the top it is marked 5 km, but there is a portion that does not have a measurement (the part with a different color than the rest. Because this line is also part of rectangle 1, we know that the line is 4 km. Adding up the two numbers gives you 9 km.
4 + 5 = 9
A = lw
A = 7 × 9
A = 63 km²
3. On the left side, it is marked 5 km. On the bottom, it is marked 20 km.
A = lw
A = 20 × 5
A = 100 km²
4. This is one is a bit more tricky. This is a triangle, so we have to find the base and the height. The base is 6 km. You have to figure the height. Look at the picture with the red lines.
The red line on the right side has a length of 17 + 3 + x = 20 + x. The length is 20 + x because there is a portion of the line that is missing.
The red lines on the left side have a length of 5 + 7 + 11 = 23. The two side should be equal so
23 = 20 + x
x = 3
Now, you have the height. Use the equation for area of a triangle to solve.
A = 1/2bh
A = 1/2(3)(6)
A = 1/2(18)
A = 9 km²
Now you have to add up all the areas to find the total area.
44 km² + 63 km² + 100 km² + 9 km² = 216 km²
Jamie needs the following items from the hardware store a drill bit that cost 4.99 nails that caused 0.46 and sandpaper that cost 0.89 how much money was spent if the sales tax rate is 6%
Answer: $5.96
Step-by-step explanation:
4.99 + 0.46 + 0.89 is what she paid, not with tax. That equals 6.34.
Applying 6% means we calculate 6% of 6.34 and then subtract it from 6.34. (Or, we can also calculate 100-6%=94% of 6.34). Either way, the answer is 5.9596, or rounded, 5.96.
Hope that helped,
-sirswagger21
A hotel with 95 room has 65 for doubles and 25 for singles. Singles can be booked in any room, but reservations for two or more people must be booked in double rooms. Let x be the number for single reservations and y the reservations for two or more. Which system of inequality represents this situation? Click the correct answer y is greater than or equal to 65 x+y less than or equal to 95 y is less than or equal to 65 x+y less than or equal to 95 x is greater than or equal to 25 x+y less than or equal to 95 x is less than or equal to 25 x+y less than or equal to 95
Answer: Y is less than or equal to 65 and X + y= less than or equal to 95
A company that manufactures video cameras produces a basic model and a deluxe model. Over the past year, 41% of the cameras sold have been of the basic model. Of those buying the basic model, 31% purchase an extended warranty, whereas 48% of all deluxe purchasers do so. If you learn that a randomly selected purchaser has an extended warranty, how likely is it that he or she has a basic model
Answer:
[tex]75.6\%[/tex]
Step-by-step explanation:
Let B be the event of buying a basic model.
Given that P(B) = 41%
Let D be the event of buying a basic model.
Given that P(D) = 1 - 41% = 59%
Let E be the event of extended warranty.
Given that:
P(E [tex]\cap[/tex] B) = 31% and
P(E [tex]\cap[/tex] D) = 48%
P(E) = P(E [tex]\cap[/tex] B) [tex]\times[/tex] P(B) + P(E [tex]\cap[/tex] D) [tex]\times[/tex] P(D)
P(E) = 31% [tex]\times[/tex] 41% + 48% [tex]\times[/tex] 59% = 0.4103
To find: P(B/E)
Formula:
[tex]P(B/E) = \dfrac{P(E \cap B)}{P(E)}[/tex]
[tex]\Rightarrow \dfrac{0.31}{0.41}\\\Rightarrow 0.756\\\Rightarrow 75.6\%[/tex]
So, the correct answer is [tex]75.6\%[/tex].
Find the volume of the prism.
The volume is cubic meters.
What is the surface area of a hemisphere with a radius 10
Answer:
Maths keeps one mentally active. The total surface of a hemisphere = 3(pi)r^2. So if the radius = 10 cm, then the TSA = 3(pi)r^2 = 300(pi) = 942.8571429 sq cm.
Step-by-step explanation:
hope this helps you :)
Answer:
The total surface of a hemisphere = 3(pi)r^2.
So if the radius = 10 cm, then the TSA = 3(pi)r^2 = 300(pi) = 942.8571429 sq cm.
What’s the correct answer for this?
Answer:
C.
Step-by-step explanation:
According to theorem, congruent angles has congruent sides opposite to them so,
RS = TU
Now
12x+4 = 11x+15
12x-11x = 15-4
So
x = 11
Now
TU = 11x+15
= 11(11)+15
= 121+15
= 136 units
A 40-foot ladder leans against a building. If
the base of the ladder is 6 feet from the
base of the building, what is the angle
formed by the ladder and the building?
Answer:
Step-by-step explanation:
draw it out and use trig function to solve for the angle. Keep in mind, after getting trig, need to do inverse
A school needs 1,860 pencils for its students. The pencils are sold in boxes of 12. How many boxes does the school need to order?
Answer:
Step-by-step explanation:
155
The number of boxes required by the school to order is 155.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We have been given that the school needs 1,860 pencils for its students. Also, the pencils are sold in boxes of 12.
We need to find the school needs to requires boxes to order.
Total number of pencil = 1,860
Number of boxes = 12
Therefore, boxes needed = 1,860 / 12
= 155
Hence, the number of boxes required by the school to order is 155.
To learn more about the unitary method, please visit the link given below;
https://brainly.com/question/23423168
#SPJ5
Assume that military aircraft use ejection seats designed for men weighing between 133.8 lb and 208.0 lb. If women’s weights are normally distributed with a mean of 172.6 lb and a standard deviation of 42.4 lb, what percentage of women have weights between the ejection seat’s weight limits (that is, 133.8 to 208.0 lb)? Enter your answer as a percent rounded to one decimal place (do not add a "%"); add a trailing zeros as needed. The percentage of women with weights between 133.8 and 208.0 lb is [EjectPct] percent.
Answer:
61.8
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 172.6, \sigma = 42.4[/tex]
What percentage of women have weights between the ejection seat’s weight limits (that is, 133.8 to 208.0 lb)?
We have to find the pvalue of Z when X = 208 subtracted by the pvalue of Z when X = 133.8 for the proportion. Then we multiply by 100 to find the percentage.
X = 208
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{208 - 172.6}{42.4}[/tex]
[tex]Z = 0.835[/tex]
[tex]Z = 0.835[/tex] has a pvalue of 0.798
X = 133.8
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{133.8 - 172.6}{42.4}[/tex]
[tex]Z = -0.915[/tex]
[tex]Z = -0.915[/tex] has a pvalue of 0.180
0.798 - 0.18 = 0.618
0.618*100 = 61.8%
Without the %, the answer is 61.8.
Answer 5x + 8 − 3x = −10
Answer:
-9
Step-by-step explanation:
5x+8-3x = -10
Combine like terms
2x+8 = -10
Subtract 8 to both sides
2x = -18
Divide both sides by 2
x = -9
Answer:
-9
Step-by-step explanation:
5x + 8 - 3x = -10
Combine like terms
2x + 8 = -10
Subtract 8 to both sides
2x = -18
Divide both sides by 2
x = -9
