[tex]7.2\:\text{ft/s}[/tex]
Step-by-step explanation:
We can apply the Pythagorean theorem here:
[tex]26^2 = x^2 + y^2\:\:\:\:\:\:\:\:\:(1)[/tex]
where x is the distance of the ladder base from the wall and y is the distance of the ladder top from the ground. Taking the time derivative of the expression above, we get
[tex]0 = 2x\dfrac{dx}{dt} + 2y\dfrac{dy}{dt}[/tex]
Solving for [tex]\frac{dx}{dt},[/tex] we get
[tex]\dfrac{dx}{dt} = -\dfrac{y}{x}\dfrac{dy}{dt}[/tex]
We can replace y by rearranging Eqn(1) such that
[tex]y = \sqrt{26^2 - x^2}[/tex]
Therefore,
[tex]\dfrac{dx}{dt} = - \dfrac{\sqrt{26^2 - x^2}}{x}\dfrac{dy}{dt}[/tex]
Since y is decreasing as the ladder is being lowered, we will assign a negative sign to [tex]\frac{dy}{dt}[/tex]. Hence,
[tex]\dfrac{dx}{dt} = - \dfrac{\sqrt{26^2 - (10)^2}}{10}(-3\:\text{ft/min})[/tex]
[tex]\:\:\:\:\:\:\:= 7.2\:\text{ft/min}[/tex]
Suppose that, in the past, 40% of all adults favored capital punishment. Do we have reason to believe that the proportion of adults favoring capital punishment today has increased if, in a random sample of 15 adults, 8 favor capital punishment? Use a 0.05 level of significance.
Answer:
The p-value of the test is 0.1469 > 0.05, which means that there is no reason to believe that the proportion of adults favoring capital punishment today has increased, using a 0.05 level of significance.
Step-by-step explanation:
Suppose that, in the past, 40% of all adults favored capital punishment. Test if the proportion has increased:
At the null hypothesis, we test if the proportion is still of 40%, that is:
[tex]H_0: p = 0.4[/tex]
At the alternative hypothesis, we test if the proportion has increased, that is, is greater than 40%, so:
[tex]H_1: p > 0.4[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.4 is tested at the null hypothesis:
This means that [tex]\mu = 0.4, \sigma = \sqrt{0.4*0.6}[/tex]
Random sample of 15 adults, 8 favor capital punishment.
This means that [tex]n = 15, X = \frac{8}{15} = 0.5333[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.5333 - 0.4}{\frac{\sqrt{0.4*0.6}}{\sqrt{15}}}[/tex]
[tex]z = 1.05[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion of 0.5333 or more, which is 1 subtracted by the p-value of z = 1.05.
Looking at the z-table, z = 1.05 has a p-value of 0.8531.
1 - 0.8531 = 0.1469.
The p-value of the test is 0.1469 > 0.05, which means that there is no reason to believe that the proportion of adults favoring capital punishment today has increased, using a 0.05 level of significance.
In a closed box there are 7 blue balls and 5 red balls. Randomly pick one from the box one at a time until the ball is green, then stop. Find the probability that the person stops after the 4th time
Answer:
1/7 is the probabiltiy
Step-by-step explanation:
help it will really hep with summer school.
Answer:
10 + 5 + 6 × 5 - 2 × 4Step-by-step explanation:
Do MDAS:10 + 5 + 6 × 5 - 2 × 4=10 + 5 + 30 - 2 × 4= 10 + 5 + 30 - 8= 15 + 30 - 8= 45 - 8= 37[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
The method of tree-ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population of x values has an approximately normal distribution.
1,2851,1871,2221,1941,2681,3161,2751,3171,275
Required:
a. Use a calculator with mean and standard deviation keys to find the sample mean year x and sample standard deviations.
b. Find a 90% confidence interval for the mean of all tree-ring dates from this archaeological site. (Round your answers to the nearest whole number.)
Answer:
a) The sample mean is 1260 and the standard deviation is 48.
b) The 90% confidence interval for the mean of all tree-ring dates from this archaeological site is (1230, 1290).
Step-by-step explanation:
Question a:
Mean is the sum of all values divided by the number of values. So
[tex]\overline{x} = \frac{1285 + 1187 + 1222 + 1194 + 1268 + 1316 + 1275 + 1317 + 1275}{9} = 1260[/tex]
Standard deviation is the square root of the sum of the differences squared between each value and the mean, divided by the one less than the sample size. So
[tex]s = \sqrt{\frac{(1285-1260)^2 + (1187-1260)^2 + (1222-1260)^2 + (1194-1260)^2 + (1268-1260)^2 + ...}{8}} = 48[/tex]
The sample mean is 1260 and the standard deviation is 48.
Question b:
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,which is the sample size subtracted by 1. So
df = 9 - 1 = 8
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 8 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.8595
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.8595\frac{48}{\sqrt{9}} = 30[/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 1260 - 30 = 1230
The upper end of the interval is the sample mean added to M. So it is 1260 + 30 = 1290
The 90% confidence interval for the mean of all tree-ring dates from this archaeological site is (1230, 1290).
linear equation 7x+25=9
Answer:
x = -16/7
Step-by-step explanation:
7x+25=9
Subtract 25 from each side
7x+25-25=9-25
7x = -16
Divide each side by 7
7x/7 = -16/7
x = -16/7
Answer:
[tex]7x + 25 = 9 \\ 7x = 9 - 25 \\ 7x = - 16 \\ x = \frac{ - 16}{7} \\ x = - 2.29[/tex]
Step-by-step explanation:
I hope it helped U
stay safe stay happy
What is the value of x?
Enter your answer in the box.
__units.
Please help click the picture to see the problem!
Using basic proportionality theorem
[tex]\\ \sf\longmapsto \dfrac{x}{10}=\dfrac{42}{15}[/tex]
[tex]\\ \sf\longmapsto 15x=42(10)[/tex]
[tex]\\ \sf\longmapsto 15x=420[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{420}{15}[/tex]
[tex]\\ \sf\longmapsto x=28[/tex]
45%of the total population of a village are males and there are 22000 females Find the male population of the village.
Answer:
18000
Step-by-step explanation:
The 22000 females make up 55% of the population. So, we divide 22000 by 0.55 to get the total population.
22000 ÷ 0.55 = 40000
Now we take our total population and subtract 22000 to get the number of males in the population.
40000 - 22000 = 18000
The male population of the village is 18000.
At the end of March, Jerry bought a plant that was $16.2 inches tall. During April, the plant grew 2] inches,
and during May, the plant grew another 2 inches. How tall was the plant at the beginning of June?
O 18.2 inches
O 19 inches
0 21 inches
21 inches
Answer:
20.2 inches
Step-by-step explanation:
The plant starts at 16.2 inches
The first month it grows 2 inches
16.2+2 =18.2 inches
Then the next month it grows 2 inches
18.2+2 = 20.2 inches
If this fish tank is filled halfway, how much water will it hold?
96 cubic inches
768 cubic inches
48 cubic inches
384 cubic inches
Answer:
384 cubic inches
Step-by-step explanation:
first find the volume of the fish tank by multipying the length, width, and height.
v=lwh
=(16in)(4in)(12in)
= 768 cubic inches (This answer is equal to the volume of the entire fish tank, however we need to find how much water half the tank can hold. To figure this out, we need to divide 768 by 2. And you should get 384 cubic inches)
Answer:
384
Step-by-step explanation:
took the quiz
The side-by-side stemplot below displays the arm spans, in centimeters, for two classes.
A stemplot titled Arm Span (centimeters). For Class A, the values are 148, 151, 153, 155, 156, 159, 161, 162, 164, 165, 169, 169, 170, 171, 175, 176, 179, 179, 180, 182, 183, 186, 186, 190. For Class B, the values are 153, 155, 16, 160, 162, 162, 162, 163, 163, 165, 166, 167, 170, 173, 180, 181, 182, 189, 192, 202.
Which statement correctly compares the variability of the arm spans for Class A to that of Class B?
The arm spans for Class A have more variability than the arm spans for Class B.
The arm spans for Class B have less variability than the arm spans for Class A.
The arm spans for Class A have less variability than the arm spans for Class B.
The arm spans for Class B have about the same variability as the arm spans for Class A.
Answer:
The answer is in the picture below
Step-by-step explanation:
Sorry just realised the answers were different ;-;
Answer:
The arm spans for Class A are roughly symmetric, while those for Class B are skewed left.
Step-by-step explanation:
HELP ASAP!!
If the circle below is cut from the square of plywood below, how many square inches of plywood would be left over?
Use π = 3.14, and round your answer to the nearest hundredth.
Answer:
13.73 in^2 because the circle's area is 50.27 in^2
Please help, question attached.
9514 1404 393
Answer:
TrueFalseStep-by-step explanation:
Dilation has no effect on angle measures, so ∠A = ∠A'.
Point A is the center of dilation, so doesn't move. Any line through point A will still go through point A after dilation. Lines AD and A'D' are not distinct.
what is the uniqueness of comeplex integration from line integaration?
Companies are starting to use 360-degree surveys to evaluate the performance of their employees. This approach uses annonymous feedback from a variety of people who work closely with the employee. People who fill out the survey could be coworkers, supervisors, subordinates, or even customers. It is different from a traditional performance review, which relies only on feedback from an employee's supervisor. Many prefer the 360-degree approach because it provides a more well-rounded perspective on how the employee performs in their job role. Supervisers can be biased because they do not interact with the employee in the same way that a customer or co-worker might. However, the 360-degree survey approach still relies only on subjective feedback, which does not always give a fair representation of the employee's work?
Answer:
the study of and knowledge about the physical world and natural lawsthe study of and knowledge about the physical world and natural lawsthe study of and knowledge about the physical world and natural lawsthe study of and knowledge about the physical world and natural laws
The quotient of three times a number and 4 is at least -16.
If anyone can help me I need to Define the variable and write an inequality, then solve.
Answer:
3x4≥−16
3x≥−64
x≥−643
x≥−2113
The answer is x≥−2113
Find hypotenuse,perpendicular and base
Answer:
Consider the angle Ф.
the line opposite to Ф is the perpendicular -> PQ = 5cm
The base is the line with whom the perpendicular has 90° angle -> PR = 12cm
Finally, hypotenuse is the line opposite to the 90° which is QR= 13cm
Answer:
hypotenuse = QR = 13 cm
Perpendicular = PQ = 5 cm
Base = PR = 12 cm
Solve for x.
A. 37
B. 27
C. 30
D. 31
Answer:
B
Step-by-step explanation:
The formula for finding the relationship between a secant and a tangent is
tangent length ^2 = external segment secant/full length of secant
In this case
60^2 = 48*(x + 48) Expand
3600 = 48*(x + 48) Remove the brackets/
3600 = 48x + 48^2 Expand
3600 = 48x + 2304 Subtract 2304 from both sides
3600 - 2304 = 48x
1296 = 48x Divide both sides by 48
1296 / 48 = x
x = 27
*20 points*
What is the probability of drawing yellow marble followed by a red marble from a bag containing 12 yellow marbles, 14 red marbles, and 15 green marbles if the first marble is not replaced?
a. 192/1,849
b. 18/43
c. 21/205
Answer:
c: 21/205
Step-by-step explanation:
The probability of choosing a yellow marble first is 12/41 bc there are 12 yellow marbles and 41 marbles to choose from.
The probability of choosing a red marble is 14/40 bc there are 14 red marbles and 40 marbles to choose from( since you have removed the marble you first chose so there are 40 marbles left).
Multiplying these two together, 12/41 * 14/40 = 168/1640, simplified it's 21/205.
Evaluate (657.3÷10)-(94.5÷5)
Answer:
Ans; (657.3÷10)-(94.5÷5) = 65.73 – 18.9 = 46.83
I hope I helped you^_^
A factory makes twenty-three million, five hundred fifty candies each month. This number in standard form is
Answer:
23,000,550
Step-by-step explanation:
A million has six zeroes, so twenty three million is
23,000,000
Since five hundred fifty is not in the thousands, it replaces the last trio of zeroes.
We have the number in standard form as
23,000,550
Answer:
23000550
Step-by-step explanation:
Use the ratio of a 45-45-90triangle to solve for the variables. Make sure to simplify radicals. Leave your answers as radicals in simplest form.
Answer:
Step-by-step explanation:
in this specific case the two legs are congruent:
b = 18
For the Pythagorean theorem
a = √ 2 * 18^2 = 18√2
(x2 + 3x + 1) + (2x2 + 2x)
HINT
Answer:
3x^2+5x+1
Step-by-step explanation:
(x^2 + 3x + 1) + (2x^2 + 2x)
Combine like terms
x^2 + 2x^2 + 3x +2x +1
3x^2+5x+1
Answer:
[tex]3x^{2} + 5x + 1[/tex]
Step-by-step explanation:
Step 1: Combine like terms
[tex](x^{2} + 3x + 1) + (2x^{2} + 2x)[/tex]
[tex](x^{2} + 2x^{2} + (3x + 2x) + (1)[/tex]
[tex]3x^{2} + 5x + 1[/tex]
Answer: [tex]3x^{2} + 5x + 1[/tex]
Please find the answer
Answer:
0.3 is the right answer.
Step-by-step explanation:
hope this helps
plz help me on this question best and right answer gets brainliest
Answer:
| - 5| 5
| 6 | 6
| - 9 | 9
the numbers will be positive when they come out from the absolute value
Answer and Step-by-step explanation:
The absolute value of a value is the positive version of that value.
| | <- Brackets are used to show that a value is being absolute.
|-5| = 5 The negative 5 with absolute brackets becomes a positive 5.
|6| = 6 A positive 6 with absolute brackets stays a positive 6.
|-9| = 9 A negative 9 with absolute brackets becomes a positive 9.
#teamtrees #PAW (Plant And Water)
Are the two triangles below similar?
U
ВО
56
No because there are not to pairs of congruent corresponding angles
Yes because there are two pairs of congruent corresponding angles
No because the corresponding sides are not proportional
Yes because the corresponding sides are proportional
Answer:
Yes, because there are two pairs of congruent corresponding angles
Step-by-step explanation:
Two triangles are similar if they have the same angles. For triangle UVT on the left, we know that the sum of angles in a triangle is 180 degrees. There is one missing angle there, so the sum of angles is
80 + 55 + missing angle = 180
subtract 80+55 = 135 from both sides
45 = missing angle
Therefore, the angles in UVT are 45, 55, and 80
Similar, for XWY,
missing angle + 45 + 55 = 180
subtract 45 + 55= 100 from both sides
missing angle = 80
The angles for XWY are 45, 55, and 80. The angles are the same for both triangles, and there are three pairs of congruent corresponding angles (45, 55, and 80). Therefore, the triangles are similar
Find the arc length of the 3/4 of a circle with a radius of 5
Answer:
7.5 pi
Step-by-step explanation:
The formula for arc length of a sector is denoted as
[tex]\frac{x}{360}2\pi r[/tex], where x is the central angle of the sector.
Since the sector is 3/4 of a circle, the central angle will be 3/4 of 360 degrees.
3/4 of 360 is 270, so we have our central angle. We also have our radius which we can plug into the formula.
[tex]\frac{270}{360}2(5)\pi[/tex]
2 times 5 is equal to 10, and 270/360 simplifies to 3/4. 3/4 times 10 is equal to 7.5, so the answer is 7.5 pi
Complete the pattern ___ 8,579 ____85.7 8.57____
Answer:
the next one is .857 I hope this helps you :)
A car is advertised with a price of $16336. The payment plan to own a car is $474 per month for 8 years. What is the
amount of interest paid?
In four years,George saved $540. His twin sister, Georgette, saved 10 times as much. How much did Georgette saved?
5400 dollars
540x10= 5400
A tortoise is walking in the desert. It walks 7.5 meters in 3 minutes. What is its speed?
meters per minute
9514 1404 393
Answer:
2.5 m/min
Step-by-step explanation:
To find meters per minute, divide meters by minutes:
(7.5 m)/(3 min) = 2.5 m/min
The speed of the tortoise is 2.5 meters per minute.
