Using the z-distribution, it is found that the desired measures are given as follows:
The test statistic is z = -0.795.The p-value is of 0.2133.What are the hypotheses tested?At the null hypotheses, it is tested if the mean is of 61.5, that is:
[tex]H_0: \mu = 61.5[/tex]
At the alternative hypotheses, it is tested if the mean is less than 61.5, that is:
[tex]H_1: \mu < 61.5[/tex]
What is the test statistic?The test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\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.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.The values of the parameters are given as follows:
[tex]\overline{x} = 59.1, \mu = 61.5, \sigma = 17.6, n = 34[/tex]
Hence, the test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{59.1 - 61.5}{\frac{17.6}{\sqrt{34}}}[/tex]
z = -0.795.
What is the p-value?We have a left-tailed test, as we are testing if the mean is less than a value, with z = -0.795. Hence, using a z-distribution calculator, the p-value is of 0.2133.
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Which expression is equal to 45 x 47 ÷4-²?
Question 6 of 10
Which of the following are not polynomials?
A,D and E are not polynomials.
Step-by-step explanation:
Well you see my friend, that's how things work.
A polynomial does not have the variable in the denominator.
|x|=x^2+x-15 solve absolute value equation and show steps please
Answer:
x=√15 or x = -5 or x=3
Step-by-step explanation:
Possibility one:
x=x^2+x-15
x-x^2=x^2+x-15-x^2 (subtract x^2 from both sides)
-x^2+x=x-15
-x^2+x-x=x-15-x (subtract x from both sides)
-x^2=-15
-x^2/-1=-15/-1 (divide both sides by -1)
x^2=15
square root both sides
x=√15 or x=-√15
Possibility two:
x=(-x^2+x-15)
x=-x^2-x+15 (simplify)
x-(-x^2-x+15)=-x^2-x+15-(-x^2-x+15) (subtract both sides by -x^2-x+15)
x^2+2x-15=0
(x-3)(x+5)=0 (factor left side of equation)
x-3=0 or x+5=0 (set factors equal to 0)
x=3 or x=-5
What is the sum of all the angles that are labeled?
Answer:
61 + 142 + 44 = 247˚
Step-by-step explanation:
Just add haha
the person above is right
Enter your answers in the boxes to correctly complete this statement.
74.94×103= (what) because the number 10³ has (what)
zeros when it is written without an exponent.
Using scientific notation, it is found that the number in standard notation is represented by:
[tex]74.94 \times 10^3 = 74940[/tex]
What is scientific notation?A number in scientific notation is given by:
[tex]a \times 10^b[/tex]
With the base being [tex]a \in [1, 10)[/tex].
In this problem, the number is given by:
[tex]74.94 \times 10^3[/tex]
Hence, applying the multiplication, we have that:
[tex]74.94 \times 10^3 = 74.94 \times 1000 = 74940[/tex]
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what is the n th term of this sequences 51,54,59,66,75,86,99
How much should be invested now at an interest rate of 6% per year, compounded continuously, to have $2500 in five years?
Answer:
$1,923.08.
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 6%/100 = 0.06 per year.
Solving our equation:
P = 2500 / ( 1 + (0.06 × 5)) = 1923.0769230769
P = $1,923.08
The principal investment required to get a total amount, principal plus interest, of $2,500.00 from simple interest at a rate of 6% per year for 5 years is $1,923.08.
What is the end behavior of the function f of x equals negative 4 times the cube root of x?
A.)As x → –∞, f(x) → –∞, and as x → ∞, f(x) → ∞.
B.) As x → –∞, f(x) → ∞, and as x → ∞, f(x) → –∞.
C.) As x → –∞, f(x) → 0, and as x → ∞, f(x) → 0.
D.) As x → 0, f(x) → –∞, and as x → ∞, f(x) → 0.
Answer:
B.) As x → –∞, f(x) → ∞, and as x → ∞, f(x) → –∞.
Step-by-step explanation:
[tex]\lim_{x\rightarrow -\infty } f\left( x\right) =\lim_{x\rightarrow -\infty } -4\sqrt[3]{x} = (-4)\times(-\infty) = +\infty[/tex]
[tex]\lim_{x\rightarrow \infty } f\left( x\right) =\lim_{x\rightarrow \infty } -4\sqrt[3]{x} = (-4)\times(+\infty) = -\infty[/tex]
sjrface area of triangle base of 11cm and height 7cm
Answer:
38.5...............
Step-by-step explanation:
(11×7)/2.
I NEED HELP PLEASEEE!!!! I HAVE BEEN WORKING ALL DAY
Answer:
188
Step-by-step explanation:
I found and fixed my mistake sorry
if the sum of 3.5 and .02 is subtracted from the product of 11 and .05 the result is
Answer:
7.53
3.5 + 0.02 = 3.52
11 + 0.05 = 11.05
11.05 - 3.52 = 7.53
PLEASE HELP ITS EXTRA CREDIT AND I COULD REALLY USE IT !! BEING TIMED! for each of the following statements, determine if the statement is true or false and explain how you decided on your answers for the polynomial.
*equation and questions included in picture below*
A. True. We see this by taking the highest order term in each factor:
[tex]f(x) = -3x(x-5)^3(x+2)^2 = -3x (x^3 + \cdots) (x^2 + \cdots) = -3x^{\boxed{6}} + \cdots[/tex]
B. True. Again we look at the leading term's degree and coefficient. f(x) behaves like -3x⁶ when x gets large. The degree is even, so as x goes to either ± ∞, x⁶ will make it positive, but multiplying by -3 will make it negative. So on both sides f(x) approaches -∞.
C. False. f(x) = 0 only for x=0, x = 5, and x = -2.
D. False. Part of this we know from the end behavior discussed in part B. On any closed interval, every polynomial is bounded, so that for any x in [-2, 5], f(x) cannot attain every positive real number.
E. True. x = 0 is a root, so f(0) = 0 and the graph of f(x) passes through (0, 0).
F. False. (0, 2) corresponds to x = 0 and f(x) = 2. But f(0) = 0 ≠ 2.
PLEASE HELP ME ANSWER THIS
Round your answer to the nearest hundredth.
Question 4 please, Thanks!
Answer:
the probability is 1.01
Select the correct answer. Which expression is equivalent to the given expression? √150
Answer:
5√6
Step-by-step explanation:
√25 x 6
√25 x√6
5√6
I need help finding the answer to this
Answer:
Step-by-step explanation:
Remark
If the figures are similar then this is a proportion question. A proportion is 2 equation ratios. The ratios can have at most 1 unknown.
Givens
DC = 7
ML = 4.9
AB = 4
JK = x
Equation
DC/ML = AB/x Substitute values into equation and solve
Solution
7/4.9 = 4/x Cross Multiply
7x = 4 * 4.9 Combine the right.
7x = 19.6 Divide by 7
7x/7 = 19.6/7
x = 2.8
Answer
x = 2.8
do a and b have the same value in the equations 2(a-1.1)=5.8 and 5/2b-2 3/4=7 1/4
Answer:
YesStep-by-step explanation:
Solve each equation and compare the solutions
1.
2(a - 1.1) = 5.8a - 1.1 = 5.8/2a - 1.1 = 2.9a = 2.9 + 1.1a = 42.
(5/2)b - 2 3/4 = 7 1/42.5b = 7 1/4 + 2 3/42.5b = 10b = 10/2.5b = 4Both a and b have same value
Answer:
Yes, a and b have the same value in the given equations.
Step-by-step explanation:
Equation 1
[tex]2(a-1.1)=5.8[/tex]
[tex]\implies 2a-2.2=5.8[/tex]
[tex]\implies 2a-2.2+2.2=5.8+2.2[/tex]
[tex]\implies 2a=8[/tex]
[tex]\implies \dfrac{2a}{2}=\dfrac{8}{2}[/tex]
[tex]\implies a=4[/tex]
Equation 2
[tex]\dfrac{5}{2}b-2\frac{3}{4}=7 \frac{1}{4}[/tex]
[tex]\implies \dfrac{5}{2}b-\dfrac{2 \times 4+3}{4}=\dfrac{7 \times 4+1}{4}[/tex]
[tex]\implies \dfrac{5}{2}b-\dfrac{11}{4}=\dfrac{29}{4}[/tex]
[tex]\implies \dfrac{5}{2}b-\dfrac{11}{4}+\dfrac{11}{4}=\dfrac{29}{4}+\dfrac{11}{4}[/tex]
[tex]\implies \dfrac{5}{2}b=\dfrac{40}{4}[/tex]
[tex]\implies \dfrac{5}{2}b=10[/tex]
[tex]\implies 2 \cdot \dfrac{5}{2}b=2 \cdot 10[/tex]
[tex]\implies 5b=20[/tex]
[tex]\implies \dfrac{5b}{5}=\dfrac{20}{5}[/tex]
[tex]\implies b=4[/tex]
Conclusion
As a = 4 and b = 4, the two variables have the same value in the given equations.
Write 2.19 as the ratio of two integers in fraction form
Answer: [tex]\frac{219}{100}[/tex]
======================================================
Explanation:
Think of [tex]2.19[/tex] as [tex]\frac{2.19}{1}[/tex] or [tex]\frac{2.19}{1.00}[/tex]
This works because dividing anything over 1 does not change the original number.
Then we can move the decimal point two spots to the right for each number
2.19 becomes 2191.00 becomes 100Therefore, [tex]2.19 = \frac{219}{100}[/tex]
The expression (cos 60°)(cos 30°) − (sin 60°)(sin 30°) can be rewritten as which of the following?
sin 30°
sin 90°
cos 30°
cos 90°
Answer:
cos 90°
Step-by-step explanation:
(cos 60°)(cos 30°) − (sin 60°)(sin 30°)
= cos ( 60° + 30°)
= cos 90°
The expression (cos 60°) (cos 30°) − (sin 60°) (sin 30°) is cos 30°.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = Perpendicular / Hypotenuse
Cosec = Hypotenuse / Perpendicular
Cos x = Base / Hypotenuse
Sec x = Hypotenuse / Base
Tan x = Perpendicular / Base
Cot x = Base / Perpendicular
We have,
(cos 60°)(cos 30°) − (sin 60°)(sin 30°)
We can use the trigonometric identity for the difference of angles between cosines.
cos(x - y) = cos(x)cos(y) - sin(x)sin(y)
By setting x = 60° and y = 30°.
So,
cos(60° - 30°) = (cos 60°)(cos 30°) − (sin 60°)(sin 30°)
cos 30° = (cos 60°) (cos 30°) − (sin 60°) (sin 30°)
Thus,
(cos 60°) (cos 30°) − (sin 60°) (sin 30°) is cos 30°.
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Why couldn't you add the
feet, yards, and centimeters
together?
Identify the equation of direct variation given that y varies directly with x. y is 75 when x is 5.
Answer:
y = 15x
Step-by-step explanation:
The equation for direct variation is ...
y = kx
where k is the constant of proportionality.
__
We can find k by dividing by x:
y/x = k
Using the given values, we find it to be ...
75/5 = k = 15
Using this value of k in the equation, we find the equation of direct variation is ...
y = 15x
Where does the energy stored in coal originally come from?
A. The Earth's Core
B. Minerals
C. The Sun
D. Radioactive material in the crust
Answer:
C . The sun
plants absorb light which make carbohydrates which makes a part of bodies of animals and plants . When they die this compound in their bodies which later became coal
(BRAINLIEST) What is the slope of the line shown in the graph?
2
−1
−fraction 1 over 2
fraction 1 over 2
Answer: the slope is y=-1/2
Step-by-step explanation:
because the line is moving from left to right, it is a negative slope
The graphically and algebraically
Find the area of the shaded portion of the sector
shown below. Round your answer to the nearest
integer
The area of the shaded region is 75.5cm^2.
The radius of the inner circle=10cm
The radius of the outer circle=14cm
angle made by sector is 90 degrees.
What is the formula for the area of the sector making an angle theta?[tex]A=\frac{\theta}{360}\times \pi r^2[/tex]
For an outer sector
[tex]Area of the sector=\frac{90}{360} \times \frac{22}{7} \times 14^2[/tex]
area of the sector=154cm^2
Now we have to find the area of the sector for the inner circle.
[tex]Area of the sector=\frac{90}{360} \times \frac{22}{7} \times 10^2[/tex]
Area of sector=78.5cm^2
Area of the shaded region =area outer sector - area of inner sector
Area of the shaded region=154-78.5.
Area of the shaded region75.5cm^2.
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The book fair is this week, and there's a special deal for teachers. For every 5 hardcover books a teacher buys, he or she can get 2 paperback books for free. Ms. Baldwin is buying 35 hardcover books for her classroom library.
How many paperback books will Ms. Baldwin get for free?
paperback books
4. Tanya Elliot purchased 400 shares of Frontier Oil at $19.00
per share and paid a $29.95 commission.
a. What was the cost of the stock?
b. What was the total paid?
a. The cost of the stock is $19
b. Tanya Elliot paid total amount of $ 7629.95.
What is cost of stock?The cost of preferred stock to a company is effectively the price it pays in return for the income it gets from issuing and selling the stock.
a. It is given that , each share= $19.00
Total number of shares = 400
Price for 400 shares be,
= 400 x $19.00
= $7600.00
Cost of the stock= [tex]\frac{ 7600}{400}[/tex]
= $19
b. Total paid by Tanya = $7600.00 +$29.95
= $7629.95
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a. What is the volume, in cubic feet, of the box in the diagram?
b. How many of these boxes can fit in the cargo hold of the truck?
Volume is a three-dimensional scalar quantity. The number of boxes that can fit in the cargo hold of the truck is 54.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The volume of the box = Volume of the cube = a³ = (2.50)³ = 15.625 ft³
The volume of cargo hold = 7.50 × 7.50 × 15 = 843.75 ft³
Now, the number of boxes that can fit in the cargo hold of the truck will be,
Number of boxes = (Volume of truck container)/(Volume of box)
= 843.75/15.625
= 54
Hence, the number of boxes that can fit in the cargo hold of the truck is 54.
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What is volume of the box in diagram (in cubic ft.)
a = 2.5ft.Volume of cube = a³
putting the value of a
Volume = (2.5ft.)³
Volume = 15.625 ft³
To find how many such boxes can be fit into the truck , we need to first find the volume of cargo hold of the truck and then divide it by the volume of 1 box
Volume of Cargo hold of truck =
= 15ft. × 7.5ft. × 7.5ft
= 843.75 ft³
No. of boxes that can be fit into the truck =
Volume of truck/ Volume of one box
= 843.75ft.3³/15.625ft.³
= 54 boxes
Daniel’s spinner is divided into 8 equal sections. A spinner divided into 8 equal sections labeled gray, green, red, purple, gray, green, yellow, blue. He plans to spin it 80 times. Which equation predicts the number of times that he could spin green? P (green) = StartFraction 1 over 8 EndFraction (80) P (green) = StartFraction 2 over 8 EndFraction (80) P (green) = StartFraction 3 over 8 EndFraction (80) P (green) = one-half (80)
We expect to get the color green 10 times out of the 80.
How many times we expect to get the color green?
The spinner is divided into 8 equal colors, so we can assume that each one of the 8 colors has the same probability of being spun.
This means that if we spin the spinner, the probability of getting the color green is p = 1/8.
So, in 80 tries, we will expect to get the color green a total of:
N = (1/8)*80 = 10
We expect to get the color green 10 times out of the 80.
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Answer:
The correct answer is P(green)=2/8 (80)
Step-by-step explanation:
Daniel’s spinner is divided into 8 equal sections.
A spinner divided into 8 equal sections labeled gray, green, red, purple, gray, green, yellow, blue.
As you can see there are 2 greens so it would be 2/8 since there are 8 pieces and 2 greens out of those 8.
HOPE THIS HELPS!
(I also did this on edge and got it correct)