Answers
I used the Pythagorean theorem to find this. 8 is the length of the given leg, and 17 is the length of the hypotenuse:
8²+b²=17²
64+b²=289
Subtract 64 from both sides:
64+b²-64=289-64
b²=225
Take the square root of both sides:
√b²=√225
b=15
Related Questions
Which of the following is the solution of 5e^2x-4=11
Answers
.. 5e^(2x) = 15
Divide by 5
.. e^(2x) = 3
Take the natural log
.. 2x = ln(3)
Divide by 2
.. x = ln(3)/2 . . . . . . . . . corresponds to the 3rd selection
The solution of the equation will be x = (ln 3) / 2. Then the correct option is C.
What is the solution of the equation?The solution of the equation means the value of the unknown or variable.
The equation is given below.
5e²ˣ – 4 = 11
On simplifying, we have
5e²ˣ = 15
e²ˣ = 3
Taking log on both sides, then we have
2x ln e = ln3
We know ln e = 1, then we have
2x = ln 3
x = (ln 3) / 2
Then the correct option is C.
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A harris poll found that 35% of people said that they drink a caffeinated beverage to combat midday drowsiness. a recent survey found that 19 out of 48 randomly selected people stated that they drank a caffeinated beverage to combat midday drowsiness. at latex-8e4a9cff882bfbfe876f36fb5b4c08e8_5a945b8082ee7.png, is the claim of the percentage found in the harris poll believable?
Answers
To determine the believability of the Harris Poll's claim that 35% use caffeine to combat drowsiness, a hypothesis test for proportions is needed. The sample proportion of 39.58% from the recent survey would be tested against the null hypothesis of 35% using a z-score calculation. Depending on if the z-score falls within the critical region, we can either reject or fail to reject the null hypothesis.
Explanation:To determine if the claim of the percentage found in the Harris Poll is believable based on the recent survey, we can conduct a hypothesis test for proportions. The null hypothesis (¿¿H₀) is that the true proportion of people who drink a caffeinated beverage to combat midday drowsiness is 35%, as stated by the Harris Poll. The alternative hypothesis (¿¿H₁) would be that the true proportion is different from 35%.
We use the information that 19 out of 48 randomly selected people stated that they drank a caffeinated beverage for midday drowsiness, which gives us a sample proportion of approximately 39.58%. To test this, we can calculate the z-score for the sample proportion and compare it to the critical value for α = 0.05 (two-tailed test). If the calculated z-score falls within the critical region, we reject the null hypothesis, indicating that the Harris Poll's claim is not believable. However, if the z-score is outside the critical region, we do not have enough evidence to reject the null hypothesis, and thus the claim is considered believable.
To perform this test, we would need to calculate the standard error for the proportion, z-score, and then compare the z-score to the appropriate critical value. Without performing the calculations here, we cannot definitively conclude about the believability of the Harris Poll's percentage claim. However, a statistician would run these numbers to reach a conclusion.
The set of life spans of an appliance is normally distributed with a mean mc013-1.jpg = 48 months and a standard deviation mc013-2.jpg = 8 months. What is the life span of an appliance that has a z-score of –3?
Answers
The formula for z-scores is:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
Using the information we're given we have:
[tex]-3=\frac{X-48}{8}[/tex]
Multiply both sides by 8 to cancel it:
-3(8) = ((X-48)/8)*8
-24 = X-48
Add 48 to both sides:
-24+48 = X-48+48
24=X
The life span of an appliance that has a z-score of –3 is 24 months if the set of life spans of an appliance is normally distributed with a mean is 48 months and a standard deviation is 8 months.
What is Z-test?The Z test is a parametric procedure that is used on data that is dispersed in a normal fashion. For testing hypotheses, the z test can be used on one sample, two samples, or proportions. When the population variance is known, it analyzes if the means of two big groups are dissimilar.
We have:
Z = -3,
[tex]\rm \mu = 48[/tex]
[tex]\sigma = 8[/tex]
We know the formula for the Z-score:
[tex]\rm Z = \frac{X-\mu}{\sigma}[/tex]
[tex]\rm-3= \frac{X-48}{8}[/tex]
-24 = X - 48
X = 24 months
Thus, the life span of an appliance that has a z-score of –3 is 24 months if the set of life spans of an appliance is normally distributed with a mean is 48 months and a standard deviation is 8 months.
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Which polynomial is in standard form
Answers
State the property that justifies the statement:
If 3x = 6, then x = 2
a. Subtraction Property of Equality
b. Addition Property of Equality
c. Division Property of Equality
d. Multiplication Property of Equality
Given that AD and BC are parallel, find the value of x.
a. 15
b. 5
c. 12.5
d. 17.5
Answers
Zero is a solution of (-1 < x < 1).
A. True
B. False
Answers
HELP!!!!!!!!!!!!!!
The ratio of the side length of Square A to the side length of Square B is 4:9. The side length of Square A is 12 yards. What is the perimeter of Square B?
Answers
4. Is the following definition of perpendicular reversible? If yes, write it as a true biconditional.
Two lines that intersect at right angles are perpendicular.
(1 point)
The statement is not reversible.
Yes; if two lines intersect at right angles, then they are perpendicular.
Yes; if two lines are perpendicular, then they intersect at right angles.
Yes; two lines intersect at right angles if (and only if) they are perpendicular.
4. Is the following definition of perpendicular reversible? If yes, write it as a true biconditional.
Two lines that intersect at right angles are perpendicular.
(1 point)
The statement is not reversible.
Yes; if two lines intersect at right angles, then they are perpendicular.
Yes; if two lines are perpendicular, then they intersect at right angles.
Yes; two lines intersect at right angles if (and only if) they are perpendicular.
@Mathematics
Answers
Is the following definition of perpendicular reversible? If yes, write it as a true biconditional.
Two lines that intersect at right angles are perpendicular.
A. The statement is not reversible.
B. Yes; if two lines intersect at right angles, then they are perpendicular.
C. Yes; if two lines are perpendicular, then they intersect at right angles.
D. Yes; two lines intersect at right angles if (and only if) they are perpendicular.
Your Answer would be (D)
Yes; two lines intersect at right angles if (and only if) they are perpendicular.
REF: 2-3 Biconditionals and Definitions
Answer:
Yes; two lines intersect at right angles if (and only if) they are perpendicular.
Step-by-step explanation:
In a biconditional statement, both parts have to be true. In this case, if the two lines intersect at a right angle then they are perpendicular, and if they are perpendicular then they intersect at a right angle
PLEASE HELP!
Fine Line Trucks rents an 18-ft truck for $42 per day plus 35¢ per mile. Judy needs a truck for one day to deliver a shipment of plants. However, she only has a budget of $70.
a) Set up an equation that models this information.
b) How many miles can Judy drive to stay within her budget?
Answers
She wants the truck for one day, which will cost $45. We don't know how far the truck is traveling so that is the variable. She cannot spend more than $70, since that is her budget.
b.) Solve for x using the above equation:
0.35x + 42 ≤ 70
0.35x ≤ 28
x ≤ 80
Judy can drive 80 miles
Devin borrowed $1,058 at 13 percent for nine months. What will he pay in interest?
A. 103.16
B.105.80
C.137.54
D.122.40
Answers
Devin borrowed $1,058 at 13 percent for nine months.
We have to calculate the interest paid.
Interest = [tex] \frac{P \times R \times T}{100} [/tex]
Substituting the values of
Principal = $1058
Rate = 13%
Time = 9 months = [tex] \frac{9}{12} [/tex] year
Interest = [tex] \frac{1058 \times 13 \times 9}{12 \times 100} [/tex]
Interest = 103.155
= 103.16
So, Devin will pay 103.16 as the interest.
Therefore, Option A is the correct answer.
If tan theta= 15/8, then:
A. sec theta = 17/8
B. cos theta = 15/17
C. cot theta = 8/15
D. csc theta = 17/15
There's potentially more than one answer.,
Answers
The only thing we have to do here is remember our trigonometric functions!
sin=y/r
cos=x/r
tan=y/x
sec=r/x
csc=r/y
cot=x/y
Knowing that tanᎾ=15/8, we know that y=15 and x=8
Now we need to look at the answer choices and see if they are correct.
A. secᎾ=17/8
Since secᎾ=r/x and r=17 and x=8, this is correct.
B. cosᎾ=15/17
Since cosᎾ=x/r and x=8 and r=17, this is wrong.
C. cotᎾ=8/15
Since cotᎾ=x/y and x=8 and y=15, this is also correct!
D. cscᎾ=17/15
Since cscᎾ=r/y and r=17 and y=15, this is right too.
I really hope this helps!
Best wishes :)
Answer:
secᎾ=17/8
cotᎾ=8/15
cscᎾ=17/15
Step-by-step explanation:
What is 65% written as a fraction in its simplest form?
Answers
(divide by 5 on both sides)
Hope this helped!
While hovering near the top of a waterfall in a national park at 46244624 feet, a helicopter pilot accidentally drops his sunglasses. the height h left parenthesis t right parenthesish(t) of the sunglasses after t seconds is given by the polynomial function h left parenthesis t right parenthesis equals negative 16 t squared plus 4624h(t)=−16t2+4624. when will the sunglasses hit the ground?
Answers
[tex]h(t)=-16 t^{2} +4624[/tex]
In order to find out when will the sunglasses hit the ground we need to solve this function for t.
We start by moving t to the left side and everything ele to the right side:
[tex]16 t^{2} =4624[/tex]
Now we divide with 16:
[tex]t^{2} =289[/tex]
Now we take square root:
[tex] t_{1} = 17s \\ t_{2} = -17s[/tex]
We ignore negative solution as time can not have negative value.
It twill take 17s seconds for the sunglassesto hit the ground.
what is the value of x will mark brain list 20 extra points
Answers
2x + 5 = 4x - 1
5 = 2x - 1
6 = 2x
3 = x
Do you get it?
PLEASE HELP ASAP!!! WILL GIVE BRAINLIEST FOR BEST/RIGHT ANSWER!!!!!!!!
Answers
a) The volleyball reached its maximum height after 3 seconds.
b) The maximum height of the volleyball was 23 feet.
c) If the volleyball is not returned by the opposing team, it will hit the ground in
5.5 seconds.
d)The graph that models the volleyball's height over time is exponential.
e) The volleyball was served for a height of 5 feet.
Answers
b) The maximum height of the volleyball was 23 feet.
e) The volleyball was served for a height of 5 feet.
Tickets for a concert sold for $8 for floor seats and $6 for balcony seats. For one performance, 400 tickets were sold, bringing in $2,888. How many of each ticket were sold?
Answers
How can categorical data for two categories be summarized?
Answers
Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
Hope this answer has helped you...
A grocer wants to make a 10-pound mixture of peanuts and cashews that he can sell for $4.75 per pound. If peanuts cost $4.00 per pound and cashews cost $6.50 per pound, how many pounds of each should he use? Let p = pounds of peanuts and let c = pounds of cashews. Write a system of equations that could be used to solve the problem.
Answers
p - pounds of peanuts
c - pounds of cashews
therefore the total pounds should be equal to 10 pounds
p + c = 10 -----> 1)
the cost for ;
peanuts - 4.00 per pound * p pounds = 4p
cashews - 6.50 per pound * c pounds = 6.5c
the price of 10 pounds mixture = 4.75 per pound * 10 pounds = 47.5
4p+6.5c = 47.5 ---> 2)
to solve for p and c lets use simultaneous equations
p + c = 10 -----> 1)
4p+6.5c = 47.5 ---> 2)
multiply 1st equation by 4
4p + 4c = 40 ---> 3)
subtract 3rd equation from the 2nd
2.5c = 7.5
c = 3
substituting c= 3 in 1st equation
p+c = 10
p+3 = 10
p = 7
therefore 3 pounds of cashews and 7 pounds of peanuts are needed to make the mixture
Picture included!
Can someone help me with these 2 questions please?
Answers
Which property is demonstrated below
Answers
Power here is another word for exponent.
Answer:
associative property of multiplication
Step-by-step explanation:
edge 2021
BRAINLIEST FOR BEST ANSWER
Answers
-10 = 2x - 8
-2 = 2x
-1 = x
You are knitting a blanket. You want the area of the planet to be 24ft^2. You want the length of the blanket to be 2ft longer than it's worth. What should the dimensions of the blanket be?
Answers
length being longer than the width means that blanket is a rectangle
width of the blanket = x
length of blanket = x +2
area = length * width
area = x * (x+2)
= x² + 2x
since area = 24
x² + 2x = 24
x² + 2x - 24 = 0
we have a quadratic equation and we need to now solve for x
x² + 6x - 4x - 24 = 0
x (x + 6) - 4(x + 6) = 0
(x-4) (x+6) = 0
x-4 = 0 or x + 6 = 0
x = 4 or x = -6
x could be either 4 or -6. since dimensions cannot have negative values,
x ≠ -6
therefore x = 4
width = 4 ft
length = 6 ft
The management of the unico department store has decided to enclose an 833 ft2 area outside the building for displaying potted plants and flowers. one side will be formed by the external wall of the store, two sides will be constructed of pine boards, and the fourth side will be made of galvanized steel fencing. if the pine board fencing costs $6/running foot and the steel fencing costs $2/running foot, determine the dimensions of the enclosure that can be erected at minimum cost. (round your answers to one decimal place.)
Answers
To maximize area and minimize perimeter, you want a figure that is as close to equilateral as you can get. Therefore we take the square root of our area:
√833 = 28.9.
Dividing 833/28.9 we get 28.8.
We want to use the shorter side, 28.8, for the pine boards, as they cost more. 28.8*2*6 = 345.60.
The cost of the steel side is given by 28.9*2 = 57.80.
Together it costs 345.60+57.80 = 403.40.
what is the slope of the line that contains the points (-1,2) and (3,3)?
A. -1/4
B. 1/4
C. 4
D. -4
Answers
the slope of the line is letter B) 1/4....
The slope of the line that contains the points (-1,2) and (3,3) is calculated using a specific formula. After performing the calculation, the result is 1/4.
Explanation:The slope of a line is calculated using a specific formula based on line's points: (y2 - y1) / (x2 - x1), where (x1,y1) and (x2,y2) are the coordinates of two distinct points on the line. In this case, the points given are (-1,2) and (3,3).
Let's substitute into the formula:
(3 - 2) / (3 - (-1)) = 1 / 4.
Therefore, the slope of the line that contains the points (-1,2) and (3,3) is 1/4, which corresponds to answer choice B.
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A circular test track for cars has a circumference of 2.7km . A car travels around the track from the southernmost point to the northernmost point. What distance does the car travel? (answer 1.35km). Part B !!!!!!!What is the car's displacement from its original position?,
Answers
The distance is how many kilometers has the car covered, the displacement is how far from the original point is the car now, and does not depend on the path followed, but it is the shortest path that connects two points.
a) In this part, they ask you for the distance. From the southernmost to the northernmost point of the circumference, the car has traveled half of the circumference, therefore:
distance = circumference ÷ 2 = 2.7km ÷ 2 = 1.35km
b) In this part, you are asked for the displacement, which in this case is the diameter of the circumference:
displacement = diameter = circumference ÷ π = 2.7km ÷ 3.14 = 0.86km = 860m
Solve for x
2/(7x) = 6/5
5/21
-21/5
21/5
I don't know
- 5/21
Answers
________________________________________
Given:
2/ (7x) = 6/5;
→ (6/5) * (7x) = 2 ;
42x / 5 = 2 ;
42x = 2*5 ;
42x = 10 ;
42x /42 = 10/42 ;
x = 10/42 = (10÷2) / (42÷2) = 5/21 ;
x = [tex] \frac{5}{21} [/tex] ;
→ which is: Answer choice: [A]: " [tex] \frac{5}{21} [/tex] " .
__________________________________________________
Find the Area of the figure
Answers
To solve this problem, we need to find the area of the circle and divide that by 2 to get the area of the semicircle, and then add that to the area of the rectangle.
First, let's find the area of the semicircle.
Since the area of a circle is calculated by pi × r^2 and diameter = 2r, we divide the diameter by 2 and plug it into the formula.
10 ÷ 2 = 5
pi × 5^2
= pi × 25
= 25pi
25pi ÷ 2 = 12.5pi
Now, let's find the area of the rectangle.
4 × 10 = 40
We add the areas together:
12.5pi + 40 = 79.27
So, the area is 79.27.
Hope this helps!
Area of a circle : pi × radius^2
r = 5
area : 78.54
but we need half of it. so divide it by 2
39.27
area of the rectangle on the bottom : 10 × 4 = 40
40 + 39.27 = 79.27
so your answer is 79.27 in²
What is the area of this triangle?
A=bh2
24 in²
30 in²
48 in²
96 in²
Right triangle with height labeled 8 inches, base labeled 6 inches, and third side labeled 10 inches.
Answers
The area formula of a triangle is:
A = [tex] \frac{1}{2} [/tex] × base × height
The given base = 6 in
The given height = 8 in
We substitute in the formula
A = [tex] \frac{1}{2} [/tex] (6)(8)
= 24 in²
Convert the angle \theta=\dfrac{23\pi}{20}θ= 20 23π theta, equals, start fraction, 23, pi, divided by, 20, end fraction radians to degrees
Answers
For this case we have the following angle in radians:
[tex] theta = \frac{23\pi}{20} [/tex]
The first thing you should know to answer the question is the following conversion:
π radians = 180 degrees
Applying the conversion to the given angle we have:
[tex] theta = \frac{23\pi}{20}*\frac{180}{\pi} [/tex]
Rewriting we have:
[tex] theta = 207 [/tex]
Answer:
the angle measured in degrees, it is given by:
[tex] theta = 207 [/tex]