A 15-foot ladder leans against the side of a house with its base 4 feet from the house. Use the Pythagorean Theorem to approximate how high the ladder reaches up the side of the house. Round your answer to the nearest hundredth.
Answers
Answer: The ladder reaches 14.46 feet up of the building.
Step-by-step explanation:
According to Pythagorean theorem,
In a right triangle,
(Hypotenuse)²= (Base)²+(perpendicular)^2
Using given information, we have
[tex](15)^2=(4)^2+(height)^2\\\\225=16+(height)^2\\\\(height)^2=209\\\\ (height)^2=\sqrt{209}\approx14.46\ feet[/tex]
Hence, the ladder reaches 14.46 feet up of the building.
Related Questions
If u + t = 5 and u-t=2, what is the value of
(u – t)(u² - 12) ?
Answers
Answer:
(u – t)(u² - 12) is equal to 0.5.
Step-by-step explanation:
First let's find u and t:
Given u + t = 5, and u - t = 2
We'll substitute one of those into the other equation.
Let's solve the second one for u:
u - t = 2
u = 2 + t
Now we can substitute that definition into the first equation:
u + t = 5
(2 + t) + t = 5
2 + 2t = 5
2t = 3
t = 1.5
Now we can substitute that into either of the original equations to find u:
u = 2 + t
u = 2 + 1.5
u = 3.5
So t = 1.5 and u = 3.5. Now we can substitute them into the given expression to solve it:
(u – t)(u² - 12)
= (3.5 – 1.5)(3.5² - 12)
= (3.5 – 1.5)(12.25 - 12)
= 2 × 0.25
= 0.5
Answer:
0.5
Step-by-step explanation:
You know that u-t is 2, so it'll be 2([tex]u^{2}[/tex] -12)
Now, system of equations to solve for u. if u+t=5, this means t=5-u, you can plug it in into u-t=2, so u-(5-u)=2. Now you know that u is 3.5, so do the calculations.
I need help with this asap thank you
Answers
Answer:a
Step-by-step explanation:a
A sample of 28 sales transactions at Costco shows a mean transaction time of 296 seconds with a standard deviation of 48 seconds. Costco is interested in finding out whether the mean transaction time is less than 310 seconds. Answer the following questions. a) Write down the null and alternative hypotheses. b) Find the test statistic and the critical value at 1% significance level. c) At 1% level of significance, what is your conclusion
Answers
Answer:
a) The null hypothesis is [tex]H_0: \mu = 310[/tex] and the alternative hypothesis is [tex]H_1: \mu < 310[/tex].
b) The test statistic is [tex]t = -1.54[/tex]. The critical value is [tex]t_c = -2.473[/tex].
c) The test statistic is [tex]t = -1.54 < t_c = -2.473[/tex], which means that there is not enough evidence to reject the null hypothesis that the mean transaction time is of 310 times, so no evidence to conclude that the mean transaction time is less than 310 seconds.
Step-by-step explanation:
Question a:
Costco is interested in finding out whether the mean transaction time is less than 310 seconds.
At the null hypothesis, we test if the mean is of 310 seconds, that is:
[tex]H_0: \mu = 310[/tex]
At the alternative hypothesis, we test if the mean is of less than 310 seconds, that is:
[tex]H_1: \mu < 310[/tex]
b) Find the test statistic and the critical value at 1% significance level.
Test if the mean is less than a value, sample of 28, and standard deviation for the sample. Thus, we have a left-tailed t-test with 28 - 1 = 27 degrees of freedom and a 0.01 significance level, and the critical value is [tex]t_c = -2.473[/tex].
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation pf the sample and n is the size of the sample.
310 is tested at the null hypothesis:
This means that [tex]\mu = 310[/tex].
A sample of 28 sales transactions at Costco shows a mean transaction time of 296 seconds with a standard deviation of 48 seconds.
This means that [tex]n = 28, X = 296, s = 48[/tex].
Value of the test statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{296 - 310}{\frac{48}{\sqrt{28}}}[/tex]
[tex]t = -1.54[/tex]
The test statistic is [tex]t = -1.54[/tex].
c) At 1% level of significance, what is your conclusion
The test statistic is [tex]t = -1.54 < t_c = -2.473[/tex], which means that there is not enough evidence to reject the null hypothesis that the mean transaction time is of 310 times, so no evidence to conclude that the mean transaction time is less than 310 seconds.
An artist wants to scale down the surface area of an image by 20%. The image initially has a length of 22 ft. and a width of 22 ft. What is the width of the scaled down image? Round to the nearest hundredth.
17.08 ft.
17.89 ft.
18.78 ft.
19.68 ft.
Answers
Answer:
17.89 ft if I'm correct.....
Answer:
D. 19.68 ftStep-by-step explanation:
Area is the product of two dimensions.
If the scale factor is k, the ratio of areas is k².
20% down means 0.8 times:
k² = 0.8k = √0.8 = 0.8944Now the width of the image is:
22*0.8944 = 19.68 ft (rounded)Correct choice is D
A birthday cake was cut into equal pieces, and five pieces were eaten. The fraction below shows how much cake was left over. According to the fraction, into how many pieces was the cake cut? 8 /13
A. 5
B. 13
C. 18
D. 8
Answers
Answer:
13
Step-by-step explanation:
Answer:
B. 13
Step-by-step explanation:
if 5 were eaten, that's 5/13, and there's 8/13 left. 5 out of thirteen total were eaten and 8 out of thirteen total were left.
How many different squads of 5 players can be picked from 10 basketball players?
Answers
Answer:
2 squads of five can be picked from 10 basketball players
Step-by-step explanation:
To solve this problem you have to divide 10 ÷ 2 which equals to 5.
The graph shows Micah’s pay for working different numbers of hours. Graph of a diagonal line on a coordinate plane with ALTDCTime worked in hoursALTDC on x-axis and ALTDCPay in dollarsALTDC on y-axis. The diagonal line is going up and to the right. Line passes through points (0, 0), (2, 30), (4, 60), A and (14, 210). A is at (8, 120) Part A What are the coordinates of Point A on the graph? Enter your answer in the boxes. ( , ) LIVE Part B What does the ordered pair for Point A represent? Use the drop-down menus to show your answer. When Micah works hours, he makes $ .
Answers
Answer:
Step-by-step explanation:
The coordinates for point A is (8,120)
This is urgent please help me out.The side lengths of different triangles are given. Which triangle is a right triangle?
Answers
Answer:
C. √18, √7, 5
Step-by-step explanation:
_____________
Find an
angle in each quadrant with a common reference angle with 146°, from
o°=0<360°
Answers
Answer:
The equivalent angle on the first quadrant is 44º. On the second quadrant, it is the given angle of 146º.
The equivalent angle on the third quadrant is 214º.
The equivalent angle on the fourth quadrant is 316º.
Step-by-step explanation:
On the first quadrant:
The equivalent in the second quadrant of a angle on the first quadrant a is 180 subtracted by the angle, that is, 180 - a.
In this question, the reference angle is 146º, which is on the second quadrant.
So, on the first quadrant:
146 = 180 - a -> a = 180 - 146 = 44.
The equivalent angle on the first quadrant is 44º. On the second quadrant, it is the given angle of 146º.
Third quadrant:
The equivalent angle on the third quadrant is 2 multiplied by 180 and subtracted by the second quadrant angle. So
2*180 - 146 = 360 - 146 = 214º.
The equivalent angle on the third quadrant is 214º.
Fourth quadrant:
The equivalent angle on the fourth quadrant is 360 subtracted by the angle on the first quadrant. So
360 - 44 = 316º
The equivalent angle on the fourth quadrant is 316º.
Find the volume of the trapezoidal prism.
7 in.
6 in.
12 in.
4 in.
Answers
Answer: 48
Step-by-step explanation: you will have to multiply
What is the perimeter of the triangle
Answers
Answer:
56 units
Step-by-step explanation:
add each side, you can get the hypotenuse using the formula a^2+b^2=c^2
Freddy earned $7.95 an hour, and last week he worked for 20 hours. About how much money did he earn?
Answers
Answer:
He earned $159
Step-by-step explanation:
7.95 Times 20
Answer:
$159
Step-by-step explanation:
[tex]\frac{1}{20} :\frac{7.95}{y}[/tex]
Cross multiply.
y · 1 = 7.95 · 20
Simplify.
y = 159
Can someone help me please.....
Answers
Answer:
the third one
Step-by-step explanation:
2 1/2
2/7, 3/4, 2/3. Arrange it in ascending order
Answers
Answer:
2,7 2,3 3/4
Step-by-step explanation:
2,7 = 0.29 2,3 = 0.67 3/4 = 0.75
Plz help me this is urgent!!
Answers
Answer:
This type of graph is B a stem graph
Answer:
B. Stem-and-leaf plot.
Step-by-step explanation:
A stem and leaf plot will typically have numbers on the left and right side, with a line separating the numbers. This graph is an example of a stem-and-leaf plot.
A line plot (example shown).
A bar graph (example shown).
A pictograph (example shown).
Goldilocks needs to find at least 12 lbs gold and 18 lbs silver to pay monthly rent. Each day in Mine 1 she finds 2 lbs gold and 2 lbs silver. Each day in Mine 2, she finds 1 lb gold and 3 lbs silver. Set up and solve using either LPsolve or on-line solver How many total days in the mines
Answers
Answer:
Total number of days in the mines = 4.5 days + 3 days ≥ 7.5 days
Step-by-step explanation:
Requirement : 12 Ibs gold and 18 Ibs silver to pay monthly rent
Mine 1 ; 2 Ibs of gold , 2Ibs of silver.
Mine 2; 1 Ib of gold , 3 Ibs of silver
using LP
Gold : aX1 + bX2 ≥ 12 ---------- ( 1 )
Silver: cX1 + dX2 ≥ 18 --------- ( 2 )
where; X1 = days spent in Mine 1
X2 = days spent in Mine 2
Total days spent in mines : X1 + X2 =
a = Gold found in mine 1 = 2
b = Gold found in mine 2 = 1
c = silver found in mine 1 = 2
d = silver found in mine 2 = 3
Back to equations 1 and 2
2X1 + X2 ≥ 12 ----------- ( 3 )
2X1 + 3X2 ≥ 18 ------------ ( 4 )
solving equations 3 and 4
= 0 + 2X2 ≥ 6 ∴ X2 ≥ 3 days ( days spent in mine 2 )
Input value into ( 3)
2X1 ≥ 12 - 3 = 9
∴ X1 ≥ 4.5 days ( days spent in mine 1 )
Total number of days in the mines = 4.5 days + 3 days ≥ 7.5 days
PLS HELP 50 POINTS
To find the amount of water that would fill the inside of an aluminum can, which of the following formulas would you use?
SA = 2 B + Ph
V = lwh
SA = 2 π r 2 + 2 π rh
V = π r 2h
Answers
Answer:
V = π r 2h
Step-by-step explanation:
The solution is, the volume of the cylinder in cubic centimeters
V = π(3.5)2h.
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
The volume of a cylinder is given by the equation:
V = π(R)^^2*h
where π = 3.14, R is the radius and h is the height.
If in the image we see that the radius is 7, then the correct option is D.
If in the image we shee that the DIAMETER is 7 (a linear that goes from end to end of the circle and goes trough the middle) then we know that the radius is half of the diameter, 7/2 = 3.5
in this case he correct option is C.
Hence, The solution is, the volume of the cylinder in cubic centimeters
V = π(3.5)2h.
To learn more on volume click :
brainly.com/question/1578538
#SPJ3
complete question:
A cylinder and its dimensions are shown. Which equation can be used to find V, the volume of the cylinder in cubic centimeters?
A) V = π(3.5h)2
B) V = π(7h)2
C) V = π(3.5)2h
D) V = π(7)2h
Answer help on this !
Answers
If the triangles are similar, then the angles are all congruent.
Therefore, we can start by setting the two middle angles equal to each other.
4x + 7 = 5x - 10
7 = x - 10
x = 17
Middle angle = 75
Now that we know our x-value, we can simply plug in x for our other two expressions.
3 * 17 = 51
4(17) - 14 = 54
We can check to make sure that our angle measures are correct by adding them all up and making sure they equal 180.
54 + 51 + 75 = 180
180 = 180
Hope this helps!! :)
Answer:
54, 51, 75
Step-by-step explanation:
4x+7=5x-10 because they are vertical angles and are therefore equal to eachother. x=17.
After plugging the 17 into the equations you get 4(17)+7=75. 3(17)=51. All angles in a triangle add up to 180. We already have 75 and 51 in the first triangle, to get the third length you need to subtract that from 180. 180-75+51=54.
The second triangle will give you the same lengths. 5x-10=75. 4(17)-14=54. Again, 180-75-54=51.
Your final lengths are 75,51,54.
Type the correct answer in the box. If cos x=sin(20 + x) and 0° <x<90°, the value of x is:
Answers
Answer:
the value of x is 90 Your answer
Step-by-step explanation:
A newly electric vehicle is designed to have a battery range of 400 miles and a standard deviation of 20 miles. assume the battery range distribution is normally distributed. the company tests 39 vehicles to determine if the battery is operating at specifications. the average range of the 39 vehicles is 398 vehicles with a standard deviation of 20 miles. find the 95% confidence interval for average battery range of the newly produced vehicle.
a) (393.72 , 406.28)
b) (391.52, 404.48
c) (393.52, 406.48)
d) (391.72, 404.28)
Answers
Answer:
b) (391.52, 404.48)
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 39 - 1 = 38
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 38 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0244
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.0244\frac{20}{\sqrt{39}} = 6.48[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 398 - 6.48 = 391.52.
The upper end of the interval is the sample mean added to M. So it is 398 + 6.48 = 404.48.
The CI is (391.52, 404.58), and the correct answer is given by option B.
Which phrase is represented by the expression 6/r+5?
A.the sum of 6 and 5 divided by a number, r
B.five more than a number, r, divided by 6
C.six divided by the sum of a number, r, and 5
D.five more than the quotient of 6 and a number, r
Answers
Answer:
D.five more than the quotient of 6 and a number,
Step-by-step explanation:
To evaluate the the phrase written as :
6/r+5
Here, there is no bracket to make any distinction, hence using the BODMAS mode of evaluation, we deal with the division first before the sum. Hence we interpr te the equation as :
6 / r = quotient ; then, 5 is added to the quotient obtained from the divison of 6 by r.
An air-conditioning fan makes 125 revolutions per second. How many revolutions will it make if it runs for 30 minutes?
Answers
Answer:
225,000 revolutions
Step-by-step explanation:
An air conditioning fan makes 125 revolutions per second
The number of revolution in 30 minutes can be calculated as follows
60 secs= 1 min
x= 30 min
= 30×60
= 1800 secs
1800×125
= 225,000
Hence the airconditioning makes 225,000 revolutions in 30 minutes
Verify the identity:
sin(A + B)
sin( A B)
tan(-4) + tan(B)
tan(4) tan(B)
Answers
Answer:
i think is the answer is
sin(A+B)
Answer:
Numerator:
sin (A + B) = sin A cos B + cos A sin BDivide by cos A cos B:
sin A /cos A + sin B /cos B = tan A + tan BDenominator:
sin (A - B) = sin A cos B - cos A sin BDivide by cos A cos B:
sin A /cos A - sin B /cos B = tan A - tan BConnect all bits together to get:
sin(A + B) / sin(A - B) = (tan A + tan B) / (tan A - tan B)PLEASEEEE HELP MEEEEEEE
Answers
Answer:
The answer is A.
Step-by-step explanation:
If you count how many blocks it takes on the y axis, you will get 7 but note that it is reflected so it is -7. If you count how many blocks it takes on the x axis you get -3. So the answer is (-3,-7).
4(q-5) = 16
help pleaseee
Answers
Answer:
q = 9
Step-by-step explanation:
the key thing to understand in this problem is the distributive property. which basically means we can muliply what's on the interior of the parenthestes ( in this case q-5) by what's on the outside (4).
so 4 will distrubute to both the q and the -5
4q - 20 = 16
add 20 to both sides
4q = 36
divide both sides by 4
q = 9
3. Find the volume of the following figure. 62 units 58 units 60 units) 64 units3
Answers
Answer:
60 units
Step-by-step explanation:
Its a 5 × 3 × 4 cube
To find volume multiply the dimensions and you will get 60
Answer:
60 units
Step-by-step explanation:
I did the test.
Mary’s bedroom rug is shown below. Find the perimeter and area of the rug.
Answers
What is the measure, in degrees, of the highlighted angle?
Answers
Answer:
[tex]36^\circ[/tex]
Step-by-step explanation:
If you add the measures of the two marked angles, you get [tex]180^\circ[/tex]. The two angles form what some call a linear pair.
Set up and solve an equation.
4x + x = 180
5x = 180
x = 180 / 5
x = 36 degrees
ILL GIVE BRAINLIEST
Given the diagram, which of the following must be true?
Answers
Answer:
Choice D
Step-by-step explanation:
QS ≈ TR
they have same direction, sense and magnitude
Answer:
B. QR ≅ TS
Step-by-step explanation:
Angle TR shows us that it is a right angle. Flip it to the other side as the inverse and we get the angle QR.
the polynomial x^+3x - 1 is a factor of x^3+2x^2-5x-6
Answers
Answer:
If its x^2 + 3x - 1 it is not a factor.
Step-by-step explanation:
x^2+3x - 1 is a factor of x^3+2x^2-5x-6?
Try dividing:
x^2+3x - 1 ) x^3 + 2x^2 - 5x - 6( x - 1
x^3 + 3x^2 - x
- x^2 -4x - 6
-x^2 - 3x + 1
- x - 7 <------- remainder.