Answer:
x = 5, 15 y = 30
Step-by-step explanation:
y=3x is the rule, thus you can use it to find all values.
15 = 3x Divide 15 by 3 in order to isolate the variable
5 = x
y = 3(10) Multiply 3 by 10 in order to find y
y = 30
45 = 3x Divide 45 by 3 in order to isolate the variable
15 = x
The cross section of a water bin is shaped like a trapezoid. The bases of the trapezoid are 21 feet and 5 feet long. It has an area of 26 square feet. What is the height of the cross section?
Answer:
2 feet
Step-by-step explanation:
We are given that
[tex]b_1=21 feet[/tex]
[tex]b_2=5feet[/tex]
Area of trapezoid=26 square ft
We have to find the height of the cross section.
We know that
Area of trapezoid=[tex]\frac{1}{2}(b_1+b_2)h[/tex]
Using the formula
[tex]26=\frac{1}{2}(21+5)[/tex]
[tex]26=\frac{1}{2}(26)h[/tex]
[tex]h=\frac{26\times 2}{26}=2 feet[/tex]
Hence, the height of cross section =2 feet
Thirty-six of the staff of 80 teachers at a local intermediate school are certified in Cardio-Pulmonary Resuscitation (CPR). In 180 days of school, about how many days can we expect that the teacher on bus duty will likely be certified in CPR?
Answer:
In about 81 days we can expect that the teacher on bus duty will likely be certified in CPR
Step-by-step explanation:
Probability of a teacher being certified in Cardio-Pulmonary Resuscitation (CPR).
36 of 80
So
[tex]p = \frac{36}{80} = 0.45[/tex]
In 180 days of school, about how many days can we expect that the teacher on bus duty will likely be certified in CPR?
45% of the days
0.45*180 = 81
In about 81 days we can expect that the teacher on bus duty will likely be certified in CPR
To calculate the number of days a teacher certified in CPR will be on bus duty, use the ratio of certified teachers (9/20) multiplied by the total number of school days (180), resulting in an expectation of 81 days.
Explanation:The student is asking to calculate the number of days one can expect a teacher certified in CPR to be on bus duty at a local intermediate school. Given that 36 out of 80 teachers are certified in CPR, the ratio of certified to non-certified teachers is 36/80, which can be simplified to 9/20. To find out how many days a teacher on bus duty will likely be certified in CPR, we apply this ratio to the total number of school days, which is 180.
Step-by-Step CalculationFirst, simplify the ratio of CPR certified teachers to the total number of teachers: [tex]36/80 = 9/20.[/tex]Next, multiply this ratio by the total number of school days to find the expected number of days: [tex]9/20 * 180 = 81.[/tex]Thus, one can expect that the teacher on bus duty will likely be certified in CPR for 81 days out of the 180 days of school.Learn more about CPR Certification Probability here:https://brainly.com/question/32753638
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8 more than the product of 12 and 4
Answer:
56
Step-by-step explanation:
The product of 2 numbers is what you get multiplying them together:
12x4 = 48
Now we need 8 more of that product so:
48 + 8 = 56
In the right triangle above a=2.7 and b=4.3. Find the value of c, rounded to the nearest tenth
Answer:
5.1
Step-by-step explanation:
Since there is no diagram provided here, we assume that c is the length of the hypotenuse, so we have ...
c² = a² +b² . . . . . . Pythagorean theorem
c² = 2.7² +4.3² = 25.78
c = √25.78 ≈ 5.0774
c ≈ 5.1
What is the surface area of this rectangular pyramid?
4 mm
5 mm
5 mm
square millimeters
To calculate the surface area of a rectangular pyramid, you need to find the base area and the areas of the triangular faces, then sum them up. In this case, the surface area of the given rectangular pyramid is 65 square millimeters.
The surface area of a rectangular pyramid is calculated by adding the base area to the sum of the areas of the four triangular faces.
Find the base area: Base area = length x width = 5 mm x 5 mm = 25 mm².Find the area of each triangular face: Use the formula A = 0.5 x base x height. Given dimensions, calculate the area of one triangle: A = 0.5 x 4 mm x 5 mm = 10 mm².Calculate the total surface area by summing base area and 4 times the area of one triangle: Total surface area = 25 mm² + 4(10 mm²) = 65 mm². Therefore, the surface area of the rectangular pyramid is 65 square millimeters.A new species of fish is released into a lake, and the fish multiply quickly. The growth of their population is modeled by the exponential function P(t) = 7bt, where t is the time in weeks after the release and b is a positive unknown base. According to the model, how many fish of the new species were released initially?
Answer:
7 fishes
Step-by-step explanation:
Given the growth of the population of fish which is modeled by the exponential function:
[tex]P(t)=7 \cdot b^t[/tex]
Where:
t=time in weeks after release
b=growth rate of the fish
At t=0
[tex]P(0)=7 \cdot b^0\\P_0=7 \cdot 1 \\P_0=7[/tex]
The initial number, [tex]P_0[/tex] of fish which was released into the lake is 7.
Use the distributive property to write the following expression WITH parentheses:
6x+18
Answer:
6(x+3)
Step-by-step explanation:
6x+18
6*x + 3*6
Factor out a 6
6(x+3)
Chairs for an orchestra are positioned in a curved form with the conductor at the center. The front row has 16 chairs, the second has 20 and the third has 24, and so on.
Answer:
The sixth term;
= 16 + (6-1)4 = 16 +20 = 36
Sixth term = 36
Pattern; a = 16, d = 4
16,20,24,28,32,36...
Completed question;
Chairs for an orchestra are positioned in a curved form with the conductor at the center. The front row has 16 chairs, the second has 20 and the third has 24, and so on. describe the pattern of the sequence. How many chairs are in the 6th row?
Step-by-step explanation:
This scenario can be represented by an arithmetic progression sequence.
nth term of an AP = a + (n-1)d
Where;
a = first term
d = common difference
n = term number
Given;
First term a = 16
Second term = a + d = 20
since a = 16
a+d = 16+d = 20
d = 20-16 = 4
The sixth term;
= 16 + (6-1)4 = 16 +20 = 36
Sixth term = 36
Pattern; a = 16, d = 4
16,20,24,28,32,36...
With this data, they test the following hypotheses. LaTeX: H_0H 0: Of Millennial students at their campus, 36% live at home with their parents. LaTeX: H_aH a: More than 36% of Millennial students at their campus live at home with their parents. In order to assess the evidence, which question best describes what we need to determine? Group of answer choices If we examine a sample of students at their campus and determine the proportion who still live at home with their parents, how likely is that proportion to be 36%? If we examine the proportion of students at their campus who still live at home with their parents, how likely is that proportion to be 36%? If we examine the proportion of students at their campus who still live at home with their parents, how likely is that proportion to be more than 36%? If we examine a sample of students at their campus and determine the proportion who still live at home with their parents, how likely is that proportion to be 43% or more? If we examine the proportion of students at their campus who still live at home with their parents, how likely is that proportion to be 43%?
Answer:
The right question that describes what we need to examine is that:
If we examine the proportion of students at their campus who still live at home with their parents, how likely is that proportion to be more than 36%?
Step-by-step explanation:
For hypthesis testing, it is the p-value that needs to be obtained, to know the significance of the result. It is in the definition of what the p-value stands for that one would be able to pick which question best describes what we need to determine?
The p-value is actually defined as the probability of obtaining results as extreme as the observed results in the statistical analysis provided that the null hypothesis is true.
It is the probability of obtaining the claim to be tested that is usually contained in the alternative hypothesis, provided the null hypothesis is true.
So, since the null hypothesis states that the proportion of Millennial students at their campus, that live at home with their parents = 36%
The p-value is how likely it is or the probability that more than 36% of Millennial students at their campus live at home with their parents.
Hope this Helps!!!
The molarity of a solute in solution is defined to be the number of moles of solute per liter of solution (1 mole = 6.02 × 1023 molecules). If X is the molarity of a solution of magnesium chloride (MgCl2), and Y is the molarity of a solution of ferric chloride (FeCl3), the molarity of chloride ion (Cl−) in a solution made of equal parts of the solutions of MgCl2 and FeCl3 is given by M = X + 1.5Y . Assume that X has mean 0.125 and standard deviation 0.05, and that Y has mean 0.350 and standard deviation 0.10.
a. Find the mean of M
b. Find the standard deviation of M (assume X and Y are independent).
Please help, need accurate solutions
Answer:
a) 0.65
b) 0.1581
Step-by-step explanation:
We are given the following in the question:
Distribution of X:
Mean = 0.125
Standard deviation = 0.05
Distribution of Y:
Mean = 0.350
Standard deviation = 0.10
Solution:
[tex]M = X + 1.5Y[/tex]
a) mean of M
[tex]\mu_M = \mu_X + 1.5(\mu_Y) = 0.125 + 1.5(0.350) = 0.65[/tex]
b) standard deviation of M
If X and Y are independent then,
[tex]Var(X+Y) = Var(X) + Var(Y)\\Var)aX) = a^2Var(X)[/tex]
[tex]Var(M) = Var(X+1.5Y)\\Var(M) =Var(X) + (1.5)^2Var(Y)\\Var(M) = (0.05)^2 + (1.5)^2(0.10)^2 = 0.025[/tex]
Standard deviation of M =
[tex]=\sqrt{Var(M)} = \sqrt{0.025} = 0.1581[/tex]
The mean of M is 0.650. The standard deviation of M is approximately 0.1581.
To find the mean of M, we need to substitute the mean values of X and Y into the equation M = X + 1.5Y. Given that X has a mean of 0.125 and Y has a mean of 0.350, we can calculate the mean of M as follows:
M = X + 1.5YM = 0.125 + 1.5(0.350)M = 0.125 + 0.525M = 0.650Therefore, the mean of M is 0.650.
To find the standard deviation of M, we can use the fact that X and Y are independent. The formula for the standard deviation of the sum of independent random variables is given by:
σM = √(σX2 + (1.5σY)2)
Given that X has a standard deviation of 0.05 and Y has a standard deviation of 0.10, we can substitute these values into the formula to calculate the standard deviation of M:
σM = √((0.05)2 + (1.5 × 0.10)2)σM = √(0.0025 + 0.0225)σM = √0.0250σM = 0.1581Therefore, the standard deviation of M is approximately 0.1581.
Data were collected on annual personal time (in hours) taken by a random sample of 16 women (group 1) and 7 men (group 2) employed by a medium sized company. The women took an average of 24.75 hours of personal time per year with a standard deviation of 2.84 hours. The men took an average of 21.89 hours of personal time per year with a standard deviation of 3.29 hours. The Human Resources Department believes that women tend to take more personal time than men because they tend to be the primary child care givers in the family. The results of the test are tequals2.02 with an associated p-value of 0.0352. The correct conclusion at alphaequals0.05 is to _______.
Answer:
We reject the null hypothesis
Step-by-step explanation:
In statistical hypothesis testing, the p-value or probability value is the probability of obtaining test results at least as extreme as the results actually observed during the test, assuming that the null hypothesis is correct
Since the p value is less than a, you would reject the null hypothesis and conclude that women take more personal time than men.
A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 240. (a) Find an expression for the number of bacteria after t hours. P(t)
Answer:
P(t) = 100e^[(ln2.4/lne)t]
or
P(t) = 100e^0.87546t
Step-by-step explanation:
see attached picture
What is the value of h(2)? -2,-1,0,3
Answer:
C
Step-by-step explanation:
Edge Trust
The value of the h(2), in the given graphed function, is determined as: C. 0.
How to Find the Value of a Function?The value of a function is the corresponding x-value of the function at that particular point or given y-value.
On the given function graph, when h(2), which is y = 2, the corresponding value of x is 0.
Therefore, the value of h(2) is: C. 0.
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Which is the equation of a parabola with Vertex (0, 0) and focus (0, 2)?
Answer:
^C
Step-by-step explanation:
The equation of a parabola with Vertex (0, 0) and focus (0, 2) is,
y = 1/8x²
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The vertex of parabola = (0, 0)
And, The focus of parabola = (0, 2)
Hence, We get;
a = 2
So, The equation of a parabola with Vertex (0, 0) and focus (0, 2) is,
x² = 4ay
x² = 4 × 2y
x² = 8y
y = 1/8x²
Thus, The equation of a parabola with Vertex (0, 0) and focus (0, 2) is,
y = 1/8x²
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4y + 1.8 = 14.7 y=
Answer:
y=1.7
Step-by-step explanation:
4y+18=14.7y
18=14.7y-4y
18=10.7y
18/10.7=10.7y/10.7
1.7=y
How many solutions does this linear system have?
y=2x-5
-8x - 4y=-20
one solution: (-2.5, 0)
one solution: (25,0)
no solution
infinite number of solutions
Answer:
The solution is (0.4;-4.2). I'm not sure since my solution is none of your alternatives, but I don't think I have made any mistakes.
Step-by-step explanation:
Replace the y at the second eq.
-8x-4(2x-5)=-20
-16x+20=-20
-16x=-40
x=0.4
Therefore y equals:
2×0.4-5=-4.2
Answer:
one solution: (2.5,0)
Step-by-step explanation:
A marketing research company is estimating the average total compensation of party clowns. Data were randomly collected from 48 party clowns and the 90% confidence interval for the mean was calculated to be ($9394, $9926). Explain what the phrase "90% confident" means.
a. 90% of the sample means from similar samples fall within the interval. In repeated sampling.
b. 90% of the intervals constructed would contain p.
c. Notes 90% of the similarly constructed intervals would contain the value of the sample mean.
d. 90% of the population values will fall within the interval.
Answer:
"90% confidence" means there is a probabilty of 90% that the population mean (average compensation for the population of party clowns) lies within the confidence interval.
Step-by-step explanation:
The confidence interval is a range of values in which, according to the level of confidence that is calculated, is likely to include a parameter of the population. In this case, this parameter is the population mean compensation of party clowns.
The level of confidence is 90%, so there is 90% of confidence (or probability) that the population mean compensation for party clowns lie within $9394 and $9926.
None of the options below is correct.
What size cop would someone with a head circumference of 570 mm need
(0,8) is the ONLY solution to the system of equations:
3y - 6x = 24
8 + 2x = y
True or False
Answer:
False, there are infinite solutions
Step-by-step explanation:
Try solving this
3y - 6x = 24
8 + 2x = y
3(8 + 2x) - 6x = 24
24 + 6x - 6x = 24
24 = 24 true
which of the following best describes the line the arrow is pointing to in the regular pentagon below? A. Leg B. Diagonal C. Base D. Apothem
Answer:
D. Apothem
Step-by-step explanation:
An Apothem is a line from the center of a regular polygon at right angles to any of its sides.
The correct describes the line the arrow is pointing to in the regular pentagon below is,
⇒ Apothem
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
We have to given that;
A regular pentagon is shown in figure.
Now, The line is vertical line.
Hence, From the center of the pentagon to the edge is called ''Apothem.''
Therefore, The correct describes the line the arrow is pointing to in the regular pentagon below is,
⇒ Apothem
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45 POINTS PLZ ANSWER!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
x = 3/4 x 21
Step-by-step explanation:
Answer:
I believe it is #2:
x = 3/4 × 21.
what is £650 in dollars
Answer:
818.87
Step-by-step explanation:
£650 = $710.76
$1.00 = £0.91
-px+r=-8x-2 solve for x.
Answer:
x = [tex]x = \frac{2+r}{p-8}[/tex]
Step-by-step explanation:
Move all terms to the left side and set equal to zero. Then set each factor equal to zero.
Answer:
(2+r)/(p-8) = x
Step-by-step explanation:
-px+r=-8x-2
Add px to each side
-px+r+px=-8x+px-2
r = -8x+px -2
Add 2 to each side
2+r = px-8x
Factor out an x
(2+r) = x(p-8)
Divide each side by (p-8)
(2+r)/(p-8) = x(p-8)/(p-8)
(2+r)/(p-8) = x
The mean annual income for people in a certain city (in thousands of dollars) is 42, with a standard deviation of 30. A pollster draws a sample of 90 people to interview. a. What is the probability that the sample mean income is less than 38?
Answer:
[tex]P(\bar X <38)[/tex]
And we can use the z score formula given by:
[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And if we find the z score for 38 we got:
[tex] z = \frac{38-42}{\frac{30}{\sqrt{90}}}= -1.265[/tex]
So then we want to find this probability:
[tex] P(z<-1.265)[/tex]
And we can use the normal standard distribution or excel and we got:
[tex] P(z<-1.265)=0.103[/tex]
Step-by-step explanation:
For this case we define the random variable X as the annual income for people at certain city. And we know the following properties:
[tex] E(X) = 42, Sd(X) =42[/tex]
They select a sample size of n = 90>30. So then we can assume that the central limit can be applied.
From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
We want to calculate this probability:
[tex]P(\bar X <38)[/tex]
And we can use the z score formula given by:
[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And if we find the z score for 38 we got:
[tex] z = \frac{38-42}{\frac{30}{\sqrt{90}}}= -1.265[/tex]
So then we want to find this probability:
[tex] P(z<-1.265)[/tex]
And we can use the normal standard distribution or excel and we got:
[tex] P(z<-1.265)=0.103[/tex]
Ezra enjoys gardening.
Let SSS represent the number of sunflower plants and LLL represent the number of lily plants Ezra's water supply can water.
0.7S+0.5L \leq 110.7S+0.5L≤110, point, 7, S, plus, 0, point, 5, L, is less than or equal to, 11
Ezra waters 101010 lily plants. How many sunflower plants can he water at most with the remaining amount of water?
Answer:
8
Step-by-step explanation:
You want to know the number of sunflower plants (S) that can be watered along with 10 lily plants (L) if the water supply is described by ...
0.7S +0.5L ≤ 11
SolutionSubstituting 10 for L, we have ...
0.7S +0.5(10) ≤ 11
0.7S +5 ≤ 11
0.7S ≤ 6
S ≤ 6/0.7 ≈ 8.57
We want to count only plants that can be watered completely, so we need to round this number to the next lower integer.
Ezra can water 8 sunflower plants with the remaining water.
when Lisa and Tom had their first child. they put $7,500 into a savings account, that earns 6% compound interest. if Lisa and Tom did not add or remove anything ,from the savings account. how much interest will they have earned after 4 years.
Answer:
$1,968.6
Step-by-step explanation:
Compound Interest = [P * (1 + i)ⁿ] - P
P = principal = $7,500
i = annual interest rate = 6%
n = number of periods = 4 years
Compound Interest = [$7,500 * (1 + 0.06)⁴] - $7,500
Compound Interest = [$7,500 * (1.06)⁴] - $7,500
Compound Interest = [$7,500 * (1.06)⁴] - $7,500
Compound Interest = [$7,500 * 1.26247696] - $7,500
Compound Interest = $9,468.5772 - $7,500
Compound Interest = $1,968.5772
An oblique hexagonal prism has a base area of 42
square cm. The prism is 4 cm tall and has an edge
length of 5 cm.
What is the volume of the prism?
cubic centimeters
5 cm
4 cm i
Answer:
168 cm³
Step-by-step explanation:
The base area of the oblique hexagonal prism = 42 cm²
the height of the prism = 4 cm
Volume of the prism = Base area × height = 42 cm² × 4 cm = 168 cm³
The volume of the oblique hexagonal prism is 260.00 cubic centimeters. This is calculated by multiplying the base area (65.00 square cm) by the height (4 cm) using the formula Volume = Base Area × Height.
To find the volume of an oblique hexagonal prism, you can use the formula:
Volume = Base Area × Height
You're given that the base area is 42 square cm and the height is 4 cm. Now, let's determine the base shape of the hexagonal prism.
A hexagon has six sides, and each side is an equilateral triangle with an edge length of 5 cm. To find the area of one of these equilateral triangles, you can use the formula:
Area of Equilateral Triangle = (side length^2 * √3) / 4
Area of Equilateral Triangle = (5 cm^2 * √3) / 4 ≈ 10.83 square cm
Since there are six identical triangles in the hexagonal base, the total base area is:
Base Area = 6 * Area of Equilateral Triangle ≈ 6 * 10.83 square cm ≈ 65.00 square cm
Now, you can calculate the volume:
Volume = Base Area × Height
Volume = 65.00 square cm × 4 cm = 260.00 cubic cm
So, the volume of the oblique hexagonal prism is 260.00 cubic centimeters.
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Answer the question bellow
Answer:
B?
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
D is not a function because for every X value, there may be more than 1 corresponding Y value past 0. For instance, if you input x=1 into this function, you get both 2 and -2, which does not make this a proper function.
Simon claims that Plant B will be taller than Plant A in 6 weeks because it has the greater initial value. Is he correct?
The answer is: No. The greater rate of change of Plant A will result in it being 0.9 inches taller in 6 weeks.
Answer:
The answer is C.
Step-by-step explanation:
what can you say about the two given equations of a line below ?
y= 2x+4
y= -1/2x+4
Answer:
y=2x+4
y=-1/2x+4
linear quations
both have the same y intercept (=4).
y=2x+4 is positive straight line, slope = 2
y=-1/2x+4 is negative straight line, slope=-1/2
Step-by-step explanation: