One afternoon the water park sold 525 tickets for a total of $13,545. Child tickets cost $19 each, and adult tickets cost $40 each. How many of each kind of ticket were sold?
Answer:
c = 355 ; a = 170
Step-by-step explanation:
c = children
a = adults
c + a = 525
19c + 40a = 13545
19c + 19a = 9975
19c + 40a = 13545
-21a = - 3570
a = 170
c + 170 = 525
c = 355
A materials engineer wants to test whether or not a certain device spends an average of more than 30 seconds soaking a component part in solution. Therefore, she goes out and takes a simple random sample of n =16 parts, and finds that the sample mean is 33.4 seconds with a sample standard deviation of s =8.0 seconds.
At α= 0.05, the Shapiro-Wilk Test for Normality has a p-value of p = 0.0667.
Suppose the engineer goes back and she selects a 17th sample unit. Using a 95% confidence level, provide the lower end point of a two-tailed interval that would be used to predict the range of values that this 17th sampled unit would be in with respect to seconds soaking a component part in solution.
Answer:
Using a 95% confidence level, the lower end point of a two-tailed interval that would be used to predict the range of values that this 17th sampled unit would be in with respect to seconds soaking a component part in solution is of 29.137 seconds.
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 = 16 - 1 = 15
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 15 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.1315
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.1315\frac{8}{\sqrt{16}} = 4.263[/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 33.4 - 4.263 = 29.137 seconds.
Using a 95% confidence level, the lower end point of a two-tailed interval that would be used to predict the range of values that this 17th sampled unit would be in with respect to seconds soaking a component part in solution is of 29.137 seconds.
What is the mean of the following numbers?
x-3a,x-2a,x-a,x,x+a
Answer:
x-a
Step-by-step explanation:
Mean=sum of data /no of data
=x-3a+x-2a+x-a+x+x+a/5
=5x-5a/5
=5(x-a)/5
=x-a
for what value of a is x-3 a factor of x^3-4x^2+ax-2a
Answer:
2x
Step-by-step explanation:
because it's2 so two ok carRy on
The value of a is 9.
What is factor?
A factor of polynomial P(x) is any polynomial which divides evenly into P(x).
How to find the solution for a polynomial?For finding the factor of a polynomial we will perform following steps:
If f(x) is any polynomial then substitute f(x) = 0.Then factorize the given polynomial by splitting the middle term. Then solve for x.According to the given question.
We have a cubic polynomial [tex]x^{3} -4x^{2} +ax -2a[/tex]
Also, x - 3a is a factor of the given polynomial.
⇒ [tex]x - 3 = 0[/tex]
⇒[tex]x = 3[/tex]
⇒ 3 is the one solution of the given cubic polynomial.
If 3 is the one solution of the cubic polynomial then it must satisfy the equation (i).
So, substitute the value of x in the given polynomial.
[tex](3)^{3} -4(3)^{2} + a (3) - 2a = 0[/tex]
⇒[tex]27 -4(3)^{2} +a(3) -2a=0[/tex]
⇒[tex]27 - 36 + 3a - 2a= 0[/tex]
⇒[tex]-9 + a = 0[/tex]
⇒ [tex]a = 9[/tex]
Therefore, the value of a is 9.
Find out more information about factor and solution of polynomial here:
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what is 4/7 x 13/9 I need help please
Answer:
0.825
Step-by-step explanation:
Answer:
52/63
hope this helps
have a good day :)
Step-by-step explanation:
Write the equation of the line that passes through the points (1, -7) and (-6, -9).
Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal
line.?
Answer:
y = 2/7 x - 51/7
Step-by-step explanation:
Equation of the line
(y-y1)/(y2-y1) = (x-x1)/(x2-x1)
(y-(-7)/(-9-(-7) = (x-1)/(-6-1)
(y+7)/-2 = (x-1)/-7
(-y-7)/2 = (-x+1)/7
-y-7 = -2/7 x + 2/7
-y = -2/7x +2/7 + 7
y = 2/7 x - 2/7 - 7
y = 2/7 x + (-2-49)/7
y = 2/7 x - 51/7
An analyst tested the null hypothesis µ ≥ 30 against the alternative hypothesis that µ < 30. The analyst reported a p-value of 0.07. For what significance level of will the null hypothesis would be rejected?
Answer:
For significance levels lower than 0.07, the null hypothesis would be rejected.
Step-by-step explanation:
Decision regarding the null hypothesis:
The decision depends on the p-value of the test.
If the p-value of the test is less than the significance level, the null hypothesis is reject.
If the p-value of the test is more than the significance level, the null hypothesis is not reject.
The analyst reported a p-value of 0.07. For what significance level of will the null hypothesis would be rejected?
From the theory above, for significance levels lower than 0.07, the null hypothesis would be rejected.
Please help image attached
A) is -4 a solution to this inequality
B) choose the correct inequality
The RAND() function in Excel returns a pseudo-random number between 0 and 1. If you enter this function into 1000 cells (i.e. enter the formula in one cell and copy it to 999 other cells), approximately how many of these cells will contain values less than or equal to 0.2?
a. A number relatively close to 1.
b. A number relatively close to 10.
c. A number relatively close to 100.
d. A number relatively close to 500.
e. A number relatively close to 1000.
Answer:
c. A number relatively close to 100.
Step-by-step explanation:
Given
[tex]Range: 0 \to 1[/tex]
[tex]N =1000[/tex] --- i.e. the cells
Required
Number of cells that contains less than or equal 0.2
Less than or equal 0.2 means that the numbers are approximately 20% of the whole distribution
So, to calculate the number (n) of these cells, we do the following computation
[tex]n = 20\% * N[/tex]
[tex]n = 20\% * 1000[/tex]
[tex]n = 200[/tex]
200 is closer to 100 than 500. Hence, (c) is correct
Evaluate n^2 -m. If you n=-5 and m=3
Answer:
22
Step-by-step explanation:
n² - m =
-5² - 3 =
25 - 3 = 22
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
22
Step-by-step explanation:
(-5)^2- 3
two negatives make a positive which would be 25 then minus the 3
=25-3
then you get your total
=22
Enter the value that will complete this expression for converting 72 inches to yards
Answer:
the answer is 12 inches
Step-by-step explanation:
there is 1 foot per 12 inches
or
12 inches make a foot
BRAINIST AND 10 POINTS
Step-by-step explanation:
12 I believe
have a great dayy
happy summee
Solve for ? Round to near whole number
Answer:
? =50
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos ? = adj/hyp
Taking the inverse cos of each side
cos^-1 (cos ?) = cos^-1( 14/22)
? =50.47880364
To the nearest degree
? =50
BRAINIEST AND 10 POINTS
Answer:
-3.125
Step-by-step explanation:
1/8 in decimal form is .125
-3 1/8 = -3.125
Work out the size of angle x
Answer:
[tex]x=47^{\circ}[/tex]
Step-by-step explanation:
By definition, parallelograms have two pairs of parallel sides. Therefore, AD and BC are parallel, and the angles marked with [tex]x[/tex] and [tex]47^{\circ}[/tex] are alternate interior angles. Since alternate interior angles are equal, we have [tex]x=\boxed{47^{\circ}}[/tex]
1 less than the square of a number.
3 is the only number which is one less than a square...
What is the equation of the graph shown above
I’ll give brainliest if you answer this right
Answer:
$16 per hour
Step-by-step explanation:
He earns $16 per hour as shown in the figure
What’s the answer and give an explanation.
Answer:
14 = x and 2.5 = y
Step-by-step explanation:
For ABCD - the top is 8 and the sides are 11. 11 minus 8 is 3. 11 plus 3 equals 14, that’s x.
For GHIJ - the bottom is 8 and both sides are 5.5. So 8 minus 5.5 is 2.5. That’s y.
Q10/ scale factor of polygon ABCD to polygon GHIJ = 11/5.5 = 2
Q11/ scale factor of polygon GHIJ to polygon ABCD = 1:2
Q12/ x = 8 × 2 = 16
y = 8 / 2 = 4
Q13/ ABCD ⇒ label x as 16, y as 4
GHIJ ⇒ label HI line to 5.5
Q14/ ratio = 46 : 23
= 2 : 1
hope this helps....
Hey does anyone know how to solve this need an answer quickly
It is believed that 25% of U.S. homes have a direct satellite television receiver. How large a sample is necessary to estimate the true population of homes which do with 95% confidence and within 3 percentage points?
Answer:
A sample of 801 is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
25% of U.S. homes have a direct satellite television receiver.
This means that [tex]\pi = 0.25[/tex]
How large a sample is necessary to estimate the true population of homes which do with 95% confidence and within 3 percentage points?
This is n for which M = 0.03. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.25*0.75}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.96\sqrt{0.25*0.75}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.25*0.75}}{0.03}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{0.25*0.75}}{0.03})^2[/tex]
[tex]n = 800.3[/tex]
Rounding up:
A sample of 801 is needed.
Use the synthetic division to find the real zeros of f(x)=2x3 +7x2+2x-3
Answer:
[tex]f(x) = {2x}^{3} + {7x}^{2} + 2x - 3 \\ f( \frac{1}{2} ) = 0 \\ f( - 3) = 0 \\ zeros \: = > 0 \: \: and \: \: - 3[/tex]
What is photosynthesis?
▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓[tex]\pmb{\qquad{\qquad{\underline{\green{\underline{\sf{Photosynthesis}}}}}}}[/tex]
Photosynthesis is the process by which green plants take in carbon dioxide and water, in the presence of chlorophyll by using sunlight to make their own food. Oxygen is released as a by product.
Chemical Reaction for PHOTOSYNTHESIS:
[tex]\sf 12H_2O + 6CO_2 \underset{chlorophyll}{\xrightarrow{Sunlight}} C_6H_{12}O_6 + 6H_2O + 6O_2 \uparrow[/tex]▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓
I need help immediately 156 1/42- 55 1/6
Answer:
100 6/7
Step-by-step explanation:
156 1/42-55 1/6
= 156 1/42 - 55 7/42
=100 36/42
=100 6/7
Answer:
100 6/7
Step-by-step explanation:
156 1/42-55 7/42
=100 36/42
=100 6/7
If x = 3, what is the value of x(14 - x)?
Answer:
33
Step-by-step explanation:
x(14 - x)
Step One: Substitute
3(14 - 3)
Step Two: Brackets/Parenthesis
3(11)
Step Three: Multiply
33
Answer:
33
Step-by-step explanation:
1. Subtract the numbers
(14-3)
2. Multiply the numbers
3*11= 33
Please help is for now
Answer:
[tex]2[/tex]
Step-by-step explanation:
Given:
[tex]-2(1-4x)=3x+8[/tex]
Let's distribute the parenthesis
[tex]-2+8x=3x+8[/tex]
Let's subtract [tex]-3x[/tex] from both sides
[tex]-2+5x=8[/tex]
Let's add [tex]2[/tex] to both sides
[tex]5x=10[/tex]
Now, let's divide both sides by [tex]5[/tex] to get [tex]x[/tex] alone
[tex]x=2[/tex]
Hope this is helpful
Step-by-step explanation:
How to solve your problem
−2(1−4)=3+8
-2(1-4x)=3x+8−2(1−4x)=3x+8
Solve
1)
Rearrange terms
−2(1−4)=3+8
-2({\color{#c92786}{1-4x}})=3x+8−2(1−4x)=3x+8
−2(−4+1)=3+8
-2({\color{#c92786}{-4x+1}})=3x+8−2(−4x+1)=3x+8
2)
Distribute
−2(−4+1)=3+8
{\color{#c92786}{-2(-4x+1)}}=3x+8−2(−4x+1)=3x+8
8−2=3+8
{\color{#c92786}{8x-2}}=3x+88x−2=3x+8
3)
Add
2
22
to both sides of the equation
8−2=3+8
8x-2=3x+88x−2=3x+8
8−2+2=3+8+2
8x-2+{\color{#c92786}{2}}=3x+8+{\color{#c92786}{2}}8x−2+2=3x+8+2
4)
Simplify
Add the numbers
Add the numbers
8=3+10
8x=3x+108x=3x+10
5)
Subtract
3
3x3x
from both sides of the equation
8=3+10
8x=3x+108x=3x+10
8−3=3+10−3
8x{\color{#c92786}{-3x}}=3x+10{\color{#c92786}{-3x}}8x−3x=3x+10−3x
6)
Simplify
Combine like terms
Combine like terms
5=10
5x=105x=10
7)
Divide both sides of the equation by the same term
5=10
5x=105x=10
55=105
\frac{5x}{{\color{#c92786}{5}}}=\frac{10}{{\color{#c92786}{5}}}55x=510
8)
Simplify
Cancel terms that are in both the numerator and denominator
A jar contains 6 red marbles numbered 1 to 6 and 8 blue marbles numbered 1 to 8. A marble is drawn at random from the jar. Find the probability the marble is red or odd numbered.
Answer:
[tex]P(R\ or\ odd\ Numbered)=5/7[/tex]
Step-by-step explanation:
From the question we are told that:
Number of Red Marble [tex]n_r=6[/tex]
Number of Blue Marble [tex]n_b=8[/tex]
Sample size [tex]n=n_r+n_b[/tex]
[tex]n=6+8[/tex]
[tex]n=14[/tex]
And
No of red or Odd numbered [tex]x= 6+4 = 10[/tex]
Generally the equation for probability the marble is red or odd numbered. is mathematically given by
[tex]P(R or odd Numbered)=x/n[/tex]
[tex]P(R or odd Numbered)=10/14[/tex]
[tex]P(R\ or\ odd\ Numbered)=5/7[/tex]
Medida de la base de un triángulo que tiene un area de 65 m2 y de altura 13 m
Answer:
10 metros.
Step-by-step explanation:
Para determinar la medida de la base de un triángulo que tiene un área de 65 metros cuadrados y una altura de 13 metros se debe realizar el siguiente cálculo, sabiendo que el área de un triangulo es igual a multiplicar su base por su altura, y dividir dicho resultado por 2:
(X x 13) / 2 = 65
X x 13 = 65 x 2
X = 130 / 13
X = 10
Por lo tanto, la base del triángulo es de 10 metros.
Find the volume of a prism
Answer:
10x7x5=350. Your answer is B! heart it if it was good!
Step-by-step explanation:
Answer:
to find the volume of a prism you need to multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.
Step-by-step explanation:
A group of three people are selected at random, what is the probability that all the three people have different birthdays.
Answer:
1:1
Step-by-step explanation:
this is because they are selected at random 3/3=1