Answer:
12
Step-by-step explanation:
[tex]-40t^2+960t-4000=1760 \\ \\ -t^2+24t-100=44 \\ \\ t^2-24t+144=0 \\ \\ (t-12)^2=0 \\ \\ t=12[/tex]
The USDA collects and distributes a wide variety of data about agriculture in the United States. One statistic reported each year is the number of milk cows (in thousands) in each state. A random sample of 10 states is selected, with the number of milk cows reported in both 2011 and 2015.
State 2011 2015 Difference
North Dakota 19 16 -3
California 1769 1778 9
Nevada 29 29 0
Ohio 268 267 -1
New Hampshire 14 14 0
Colorado 128 146 18
Minnesota 468 460 -8
Oklahoma 53 39 -14
Utah 93 96 3
Washington 260 277 17
mean 310.1 312.2 2.1
sd 532.857 535.367 10.159
An agricultural researcher wants to conduct a paired difference test to determine if the mean number of milk cows (in thousands) in the US changed between 2011 and 2015.
Round all calculated values to 4 decimal places as appropriate.
1. Which hypotheses should be used to conduct the test?
A. H0:μdiff=0 vs. Ha:μdiff≠0
B. H0:μdiff<2.1 vs. Ha:μdiff>2.1
C. H0:μdiff=0 vs. Ha:μdiff<0
D. H0:μdiff=0 vs. Ha:μdiff>0
2. Assume the conditions for the hypothesis test are met and find the test statistic and the p-value.
test statistic =
p-value =
3. Based on the p value we have
?
evidence that the null model is not a good fit for our observed data.
4. Construct a 99% confidence interval for the mean difference in the number of milk cows (in thousands) between 2011 and 2015.
1. The hypothesis tested are given as follows: A. H0:μdiff=0 vs. Ha:μdiff≠0.
2.
The test statistic is of: t = 0.65.The p-value is of: 0.26603. Based on the p-value, we do not have enough evidence that the null model is not a good fit for our observed data.
4. The 99% confidence interval for the mean difference in the number of milk cows (in thousands) between 2011 and 2015 is of (-8.34, 12.54).
What are hypothesis tested?At the null hypothesis, it is tested if there has not been change, that is, if the mean is of zero, hence:
H0:μdiff=0
At the alternative hypothesis, it is tested if there has been change, hence:
Ha: μdiff≠0
Considering a two-tailed test, as we are testing if the mean is different of a value, with 10 - 1 = 9 df, and a significance level of 1 - 0.99 = 0.01, the critical value is of:
|t| = 3.25.
What is the test statistic?The test statistic for the t-distribution is given by the equation presented as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.The parameters in this problem are given as follows:
[tex]\overline{x} = 2.1, s = 10.159, n = 10, \mu = 0[/tex]
Hence the test statistic is of:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{2.1 - 0}{\frac{10.159}{\sqrt{10}}}[/tex]
t = 0.65.
What are the p-value and the conclusion?Considering a two-tailed test, with t = 0.65 and 10 - 1 = 9 df, the p-value is of:
0.2660.
What is the confidence interval?The confidence interval is given as the estimate plus/minus the multiplication of the critical value and the standard error.
Hence the lower bound of the interval is of:
2.1 - 3.25x10.159/sqrt(10) = -8.34.
The upper bound of the interval is of:
2.1 + 3.25x10.159/sqrt(10) = 12.54.
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im on a bit of a time crunch so please hurry :)
Answer
39 child tickets were sold that day
Step-by-step explanation
Variables
• x: child tickets sold
,• y: adult tickets sold
Given that four times as many adult tickets as child tickets were sold, then:
[tex]y=4x[/tex]If 1 child ticket cost $5.70, then x child tickets will cost 5.7x dollars.
If 1 adult ticket cost $9.20, then y adult tickets will cost 9.2y dollars.
Given that the theater sold tickets for $1657.50, then:
[tex]5.7x+9.2y=1657.5[/tex]Substituting the first equation into the second one and solving for x:
[tex]\begin{gathered} 5.7x+9.2(4x)=1,657.5 \\ 5.7x+36.8x=1,657.5 \\ 42.5x=1,657.5 \\ \frac{42.5x}{42.5}=\frac{1,657.5}{42.5} \\ x=39 \end{gathered}[/tex]A sample was done, collecting the data below. Calculate the standard deviation, to one decimalplace.х24726573
We have the following data
[tex]24,7,26,5,13[/tex]The standard deviation is given by
[tex]\sigma=\sqrt[]{\frac{\sum(x_i-\mu)^2}{N}}[/tex]Where μ is the mean and N is the number of data points
Let us first find the mean of the data.
[tex]\mu=\frac{\text{sum}}{number\text{ of data points}}=\frac{24+7+26+5+13}{5}=\frac{75}{5}=15[/tex]Finally, the standard deviation is
[tex]\begin{gathered} \sigma=\sqrt[]{\frac{(24-15)^2+(7-15)^2+(26-15)^2+(5-15)^2+(13-15)^2}{5}} \\ \sigma=\sqrt[]{\frac{(9)^2+(-8)^2+(11)^2+(-10)^2+(-2)^2}{5}} \\ \sigma=\sqrt[]{\frac{81^{}+64^{}+110^{}+100^{}+4^{}}{5}} \\ \sigma=\sqrt[]{\frac{359}{5}} \\ \sigma=\sqrt[]{71.8} \\ \sigma=8.5 \end{gathered}[/tex]Therefore, the standard deviation of the data set is 8.5
Question #10: Given triangle A is the pre image and B is the image, state the scale factor of the dilation from A to B. * 4 B 10 18 А 7.2 15
To find the acale factor we need to solve the following equation:
[tex]\begin{gathered} 18k=7.2 \\ k=\frac{7.2}{18} \\ k=0.4 \end{gathered}[/tex]This comes from the fact that the biggest sides of both triangles have to be realted.
Therefore the dilation factor is 0.4.
A 3 dimensional shape is created when the shape isrotated around the y-axisFind the volumen of shape
By rotating the shape of the graph, we get the following cylinder:
So we have a cylinder with:
• radius r = 4,
,• height h = 6.
The volume of the cylinder using π = 3.14 is given by:
[tex]V=\pi *r^2*h=3.14*4^2*6=301.44.[/tex]AnswerThe solid obtained is a cylinder of volume 301.44.
I have 3 more questions but it didn’t fir here
Probability = number of required outcome/number of the possible outcome
(a) To determine the theoretical probability for mary
[tex]\begin{gathered} \text{ Probability of spinner landing on grey = }\frac{\text{ number of grey}}{Total\text{ colour}} \\ \text{Probability of spinner landing on grey = }\frac{593}{1000} \\ \text{Probability of spinner landing on grey = 0.}593 \end{gathered}[/tex](b) To determine the experimental probabiity for mary's result
[tex]\begin{gathered} \text{Experimental probabil}ity\text{ = }\frac{\text{ number of grey}}{Total\text{ number}} \\ \text{Experimental probabil}ity\text{ = }\frac{3}{5\text{ }} \\ \text{Experimental probabil}ity=\text{ 0}.600 \end{gathered}[/tex](c) Assuming the spinner is fair, with a large number of spins there might be a difference between the experimental and theoretical probability but the difference will be small.
someone please help I don't get it!!
Answer:
which one
Step-by-step explanation:
don't forget to follow rate like
A standard pair of six sided dice is rolled what is the probability of rolling a sum greater than or equal to 11
The diagram below shows all the possible outcomes from rolling a pair of six sided dice.
The first row and first columns represents the numbers on each die. The numbers in the other rows and columns are outcomes for each roll. Thus, the total number of outcomes is the total number of pairs in the other rows and columns.
Total number of outcomes = 36
Number of outcomes with sum greater than or equal to 11 are the circled pairs. They are 3
Thus, the probability of rolling a sum greater than or equal to 11 is
3/36 = 1/12
A randomly generated list of integers from O to 4 is being used to simulate anevent, with the number 3 representing a success. What is the estimatedprobability of a success?
We have that:
• A randomly generated list of, integers from 0 to 4 i,s being used to simulate an event.
• The number 3 represents a success.
And we need to find the estimated probability of success.
We can achieve that if we know that:
1. We have the following sample space for the experiment - we have a list of integers from 0 to 4:
[tex]\Omega=\lbrace0,1,2,3,4\rbrace[/tex]2. Then the probability of having a 3 is:
[tex]P(3)=\frac{1}{5}=0.2\Rightarrow20\%[/tex]We have one possibility of getting a 3 (one possibility) out of 5 possibilities (0, 1, 2, 3, 4).
Therefore, the estimated probability of success is 20% (option D.)
i need to know which one is the answer , i’m having a hard time figuring it out
Answer:
Explanation:
Here, we want to know the table that represents a function
For a relationship to represent a function, no two y values can have a single x value but two x values can have a single y value.
What this means is that two independent variable values can take a single dependent variable value but no two dependent variable values can take a single independent variable value
Now, looking at the table given:
What is the solution to the linear equation 2/5+p=4/5+3/5p
Ok ,we need to find p in the following equation: 2/5+p=4/5+3/5p, lets
Given two vectors,find y so that a and b are orthogonal,
In they are orthogonal the their scarlar product will be zero.
So
[tex]a\cdot b=0[/tex][tex]\begin{gathered} (9,-7,-7)\cdot(6,y,-4)=0 \\ 54-7y+28=0 \\ -7y=-82 \\ y=11.714 \end{gathered}[/tex]Hence, [tex]y=11.714[/tex] when the [tex]a[/tex] and [tex]b[/tex] are orthogonal.
What is the vectors?
Vectors in math is a geometric entity that has both magnitude and direction. Vectors have an initial point at the point where they start and a terminal point that tells the final position of the point.
Various operations can be applied to vectors such as addition, subtraction, and multiplication.
Here given that,
[tex]a=(9,-7,-7)\\b=(6,y,-4)[/tex]
If they are orthogonal the their scarlar product will be zero.
So,
[tex](9,-7,-7).(6,y,-4)=0\\54-7y+28=0\\-7y=-82\\As,\\a.b=0\\y=\frac{82}{7}\\y=11.714[/tex]
Hence, [tex]y=11.714[/tex] when the [tex]a[/tex] and [tex]b[/tex] are orthogonal.
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Write the slope-intercept (y = mx + b) form of an equation for a line with y-intercept-5 and slope 2.
The slope-intercept form of the line is
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept
so we only need to substitute the values into the equation
m=2
b= -5
the equation is
[tex]y=2x-5[/tex]The volume of gas kept at a constant pressure varies inversely with the temperature T. If the temperature is 50 degrees, the volume is 20 quick feet. What will the volume be when the temperature is 100 degrees. V= , Temperature=. . Solution
Given that the volume of gas kept at constant pressure varies inversely with the temperature T and when the temperature is 50 degrees, the volume is 20 cubic feet.
We have to find the volume of gas when the temperature is 100 degrees.
Since it is given that volume varies inversely with the temperature. It means
[tex]T_1V_1=T_2V_2[/tex]Substitute T1 = 50, V1 = 20, T2 = 100.
[tex]\begin{gathered} 50\times20=100\times V_2 \\ 1000=100\times V_2 \\ \frac{1000}{100}=V_2 \\ 10=V_2 \end{gathered}[/tex]Thus, the volume of gas when the temperature is 100 degrees is 10 cubic feet.
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 4)-1 and 3 + 2i A) (x)= x3 + 5x2 +7x + 13 B)(x) = x3 - 5x2 + 7x - 13 C)(x)= x3 - 5x2 + 7x + 13 D) f() = x3 - 5x2 + 7x + 14
trey is draining an aquarium. the graph shows the amount of water (in liters) in the aquarium versus time (in minutes)
Given the graph represents the amount of water in the aquarium versus time.
A) As shown in the graph :
as the time increases the amount of water in the aquarium decreases
The rate of water decreasing =
[tex]\frac{480}{8}=60[/tex]so, the rate = 60 litres per minute
Find the equation for the line that passes through the point (3.-5), and that is perpendicular to the line with the equation x = -2
• Line x = -2 is a vertical line that passes through point x = -2
Given the point ( 3;-5)
• We know that perpendicular lines have opposite reciprocal slopes , so the slope of the line will be
,• m = 1/2
• so , the standard formula for a line : y = mx +c
at point ( 3-5) , we will have :
-5 = 1/2(3) + c
Therefore c = -5 -3/2
= -13/2
• Our y- intercept will be -13/2
• Finally , our equation of the line will be :
y = 1/2x -13/2
Mia made a pencil box in the shape of a right rectangular prism what's the surface area of the box 20cm,6cm,7cm
1) Let's visualize it to better understand:
A right rectangular prism is made from
2 faces 6 x 7
4 faces 20 x 6
Since we have rectangles, we can write calculating the area of each rectangle.
S base = 2 (6x 7) ⇒ S base = 84 cm²
S faces = 2 (20 x 6) ⇒ S faces = 240 cm²
S faces = 2 (20 x 7) ⇒ S faces = 280 cm²
2) Then the total surface area
84+240+280=604 cm²
what does translation mean?
translation means moving a geometric object in the cartesian plane without rotating it.
the density of aluminum is 2700 kg/m3. what is the mass of a solid cube of aluminum with side lengths of 0.5 meters?
SOLUTION
Density is calculated as
[tex]\begin{gathered} Density=\frac{mass}{volume} \\ \end{gathered}[/tex]The side lengths of the aluminium cube has been given as 0.5 m
The volume becomes
[tex]\begin{gathered} volume=length\times length\times length \\ V=L\times L\times L \\ V=0.5\times0.5\times0.5=0.125m^3 \end{gathered}[/tex]so the volume is 0.125 cubic-meters.
The mass becomes
[tex]\begin{gathered} Density=\frac{mass}{volume} \\ mass=density\times volume \\ mass=2700\times0.125 \\ =337.5 \end{gathered}[/tex]Hence the answer is 337.5 kg
If the rate of inflation is 2.5% per year, the future price P(T) in dollars of a certain item can be modeled by the following exponential function, where T is the number of years from today
Solution:
The future price p(t), in dollars, can be modelled by the exponential function;
[tex]p(t)=800(1.025)^t[/tex](a) The current price is;
[tex]\begin{gathered} t=0; \\ \\ p(0)=800(1.025)^0 \\ \\ p(0)=800(1) \\ \\ p(0)=800 \end{gathered}[/tex]ANSWER: $800
(b) The price 8 years from today;
[tex]\begin{gathered} t=8 \\ \\ p(8)=800(1.025)^8 \\ \\ p(8)=800(1.2184) \\ \\ p(8)=974.72 \\ \\ p(8)\approx975 \end{gathered}[/tex]ANSWER: $975
f(×) = 3× + 7 f(1) =
f(1) = 10
Explanation:Given f(x) = 3x + 7
To find f(1), replace x by 1 in the equation above
f(1) = 3(1) + 7
= 3 + 7
= 10
Determine if the triangles, △YPQ and △NPD, are similar. if so, Identify criterion.
Answer:
Yes, they are similar.
Criterion: AA Similarity
Explanation:
Looking at triangles YPQ and NPD, we can see that angles NPD and YPQ are vertically opposite angles and are congruent since vertically opposite angles are always congruent;
[tex]\angle YPQ\cong\angle NPD\text{ (vertically opposite angles)}[/tex]We can also observe that angles N and Y are congruent since they are alternate angles;
[tex]\angle N\cong\angle Y\text{ (alternate angles)}[/tex]From the AA similarity rule, we know that two triangles are said to be similar if two angles in one triangle are equal to two triangles in the other triangle.
Therefore, from the AA rule, we can say that triangles YPQ and NPD are similar.
Which triangle congruence postulate or theorem proves that these triangles are congruent?
The AAS triangle congruence postulate proves that these triangles are congruent .
In the question,
two triangles are given that are triangle ABC and triangle PQR .
Consider the triangle ABC and triangle PQR .
we can see that
(i) angle C = angle R .....given in the figure
(iii) angle B = angle Q .... given in the figure
(ii) side BC = side QR ....given in the figure
From the above three statements we conclude that
ΔABC ≅ ΔPQR
both the triangles KLM and PQR are congruent by AAS Congruence Postulate .
Therefore , The AAS triangle congruence postulate proves that these triangles are congruent .
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4x + 8 = 28Describe a real-world situation the equation could represent.
In a club, the entrance ticket is $8. And every time you order a soda you have to pay $4 per can. Since you only have $28 in your pocket, how many sodas can you afford?
The equation 4x +8=28 could be used to describe a scenario like this below:
In a club, the entrance ticket is $8. And every time you order a soda you have to pay $4 per can. Since you only have $28 in your pocket, how many sodas can you afford?
Notice the fixed amount (8) and the variable (4x) and the total of money you have (28). So the sum above describes the amount of money for that club.
With that equation you can find that:
4x +8=28
4x+8 -8 =28-8
4x=20
x=5
5 cans of soda.
Two jets leave harrisburg at the same time, one flying east at a speed of 20 km/h greater than the other, which is flying west. After 4 h, the planes are 6000 km apart. Find their speeds. A tourist bus leaves Richmond at 1:90 PM for New York City. Exactly 24 minutes later, a truck sets out in the same direction. The tourist bus moved at a steady 60 km/h. The truck travels at 80 km/h. How long does it take the truck to overtake the tour bus?
We know that two jets leave Harrisburg at the same, time, one flying east, and another flying west.
We will denote the speed of the second jet by x (in km/h). Thus, the speed of the first jet is x+20. Remembering that:
[tex]v=\frac{d}{t}[/tex]where v is speed, d is distance and t is time, we know that for the first jet:
[tex]x+20=\frac{d_1}{4}\Rightarrow4x+80=d_1[/tex]Where d₁ represents the distance of the first jet from the starting point. For the second jet:
[tex]x=\frac{d_2}{4}\Rightarrow4x=d_2[/tex]Where d₂ represents the distance of the second jet from the starting point.
We also know that:
[tex]d_1+d_2=6000[/tex]As:
Thus, we have that:
[tex]\begin{gathered} (4x+80)+(4x)=6000 \\ \text{And solving for x, we get:} \\ 8x+80=6000 \\ 8x=5920 \\ x=\frac{5920}{8}=740 \end{gathered}[/tex]This means that the second jet has a speed of 740km/h, and the first jet has a speed of 760km/h (20km/h greater than the second one).
The population of Boom town is 775,000 and is increasing at a rate of 6.75% each year. How many years will it take to reach a population of 1,395,000?
To study population growth, we use the following formula
[tex]P=P_0\cdot e^{rt}[/tex]Where,
[tex]\begin{gathered} P=1,395,000 \\ P_0=775,000 \\ r=0.0675 \end{gathered}[/tex]Let's replace the values above, and solve for t.
[tex]\begin{gathered} 1,395,000=775,000\cdot e^{0.0675t} \\ e^{0.0675t}=\frac{1,395,000}{775,000} \\ e^{0.0675t}=1.8 \\ \ln (e^{0.0675t})=\ln (1.8) \\ 0.0675t=\ln (1.8) \\ t=\frac{\ln (1.8)}{0.0675} \\ t\approx8.7 \end{gathered}[/tex]Hence, it would take 8.7 years to reach a population of 1,395,000.Write the point-slope form of the equation of the line through the points (-1, -1) and (2, 4)
The point-slope form of (-1, -1) and (2, 4) is y = 5/3(x+1) - 1.
The point-slope form is simply writing an equation of a line so that the slope or steepness and x-intercept i.e. where the line crosses the vertical x-axis are immediately apparent.
The slope-intercept equation is y - y1 = m(x - x1), where x and y are two variables, and m is the slope.
Slope m = (y2-y1) / (x2-x1)
Let,
(x1, y1) = (-1, -1)
(x2, y2) = (2, 4)
Slope (m) = ((4) - (-1)) / ((2) - (-1))
= 5/3
y - y1 = m(x - x1) => (y - (-1)) = 5/3(x - (-1))
=> y+1 = 5/3(x + 1)
=>y = 5/3(x+1)-1
Therefore, the point-slope form of (-1, -1) and (2, 4) is y = 5/3(x+1)-1.
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-2( 4 - 6h ) +9-8 - 12h + 9-12h + 1Explain the error in the work.
The error is in the distribution property application, in the way the signs are multiplied.
We will look at it in detail:
[tex]\begin{gathered} -2(4-6h)+9 \\ \lbrack(-2)(4)+(-2)(-6h)\rbrack+9 \\ (-8+12h)+9 \\ 12h+1 \end{gathered}[/tex]When (-2) is multiplied by (-12h) it should end with a positive sign, as (-a)*(-b)=a*b
I am having a hard time finding the apt for this question pls help me?
The APR, that is Annual Percentage Rate, is calculated using the formula below;
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