Answer:
The legs of a 45 45 90 are equal
And the length of the hypotenuse equals
leg * square toot of 2
Step-by-step explanation:
The fuel consortium chairman at an airport recorded the cost per barrel of crude oil and the cost per barrel of jet fuel each week.
After plotting his results, the chairman noticed that the relationship between the two variables was fairly linear, so he used the data to calculate the following least squares regression equation for predicting the cost, in dollars, per barrel of jet fuel from the cost, in dollars, per barrel of crude oil.
y^=2+7/6x
What is the residual of a week in which a barrel of crude oil costs $60 and a barrel of jet fuel costs 78$. THE ANSWER IS $6!!
Answer:
Residual for the week will be $6.
Step-by-step explanation:
Regression equation predicting the per barrel cost of jet fuel is,
[tex]\hat{y}=2+\frac{7}{6}x[/tex]
where, [tex]\hat{y}[/tex] = cost of jet fuel
x = cost of crude oil per week
If the cost of crude oil in any week = $60
Then predicted cost of jet fuel,
[tex]\hat{y}=2+[\frac{7}{6}\times (60)][/tex]
= 2 + 70
= $72
Residual price = Actual cost - predicted cost
= $78 - $72
= $6
Therefore, residual price will be $6.
The residual of the week in which a barrel of crude oil costs $60 is $6
The least square regression equation is given as:
[tex]\mathbf{\^y = 2 + \frac 76x}[/tex]
When a barrel of crude oil costs $60, it means that x = 60.
So, we have:
[tex]\mathbf{\^y = 2 + \frac 76 \times 60}[/tex]
[tex]\mathbf{\^y = 2 + 7 \times 10}[/tex]
Multiply
[tex]\mathbf{\^y = 2 + 70}[/tex]
Add
[tex]\mathbf{\^y = 72}[/tex]
So, we have:
Actual Cost = $78
Predicted Cost = $72
The residual is then calculated as:
[tex]\mathbf{Residual = Actual - Predicted }[/tex]
This gives
[tex]\mathbf{Residual = \$78 - \$72}[/tex]
Subtract
[tex]\mathbf{Residual = \$6}[/tex]
Hence, the residual of the week is $6
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A manufacturer of a new medication on the market for Crohn's disease makes a claim that the medication is effective in 85% of people who have the disease. One hundred seventy-five individuals with Crohn's disease are given the medication, and 135 of them note the medication was effective. Does this finding provide statistical evidence at the 0.05 level that the effectiveness is less than the 85% claim the company is making? Make sure to include parameter, conditions, calculations, and a conclusion in your answer. (10 points)
Answer:
We conclude that the effectiveness is less than the 85% claim the company is making.
Step-by-step explanation:
We are given that a manufacturer of a new medication on the market for Crohn's disease makes a claim that the medication is effective in 85% of people who have the disease.
One hundred seventy-five individuals with Crohn's disease are given the medication, and 135 of them note the medication was effective.
Let p = percentage of people who have the Crohn's disease.
So, Null Hypothesis, [tex]H_0[/tex] : p = 85% {means that the effectiveness is equal to the 85% claim the company is making}
Alternate Hypothesis, [tex]H_A[/tex] : p < 85% {means that the effectiveness is less than the 85% claim the company is making}
The test statistics that would be used here One-sample z proportion statistics;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of individuals who note the medication was effective = [tex]\frac{135}{175}[/tex] = 0.77
n = sample of individuals with Crohn's disease taken = 175
So, test statistics = [tex]\frac{0.77-0.85}{\sqrt{\frac{0.77(1-0.77)}{175} } }[/tex]
= -2.515
The value of z test statistics is -2.515.
Now, at 0.05 significance level the z table gives critical value of -1.645 for left-tailed test.
Since our test statistic is less than the critical value of z as -2.515 < -1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the effectiveness is less than the 85% claim the company is making.
The study's findings suggest that the medication is less effective than the manufacturer's claim of 85%.
Step-by-Step Calculation
1. Define the parameter
The parameter we are testing is the population proportion p of people with Crohn's disease for whom the medication is effective. The manufacturer's claim is that [tex]\( p = 0.85 \)[/tex].
2. State the hypotheses
- Null hypothesis [tex]\( H_0 \): \( p = 0.85 \)[/tex]
- Alternative hypothesis [tex]\( H_a \)[/tex] : [tex]\( p < 0.85 \)[/tex]
3. Check conditions for the test
We use a one-sample z-test for proportions. The conditions are:
- Random sample: Assume the sample is random.
- Large enough sample size: Both [tex]\( np \)[/tex] and [tex]\( n(1-p) \)[/tex] should be greater than 10.
Calculations:
- [tex]\( np = 175 \times 0.85 = 148.75 \)[/tex]
- [tex]\( n(1-p) = 175 \times 0.15 = 26.25 \)[/tex]
Both values are greater than 10, so the conditions are met.
4. Perform the calculations
Sample proportion [tex]\( \hat{p} \)[/tex]:
[tex]\[ \hat{p} = \frac{135}{175} = 0.7714 \][/tex]
Standard error (SE) of the sampling distribution:
[tex]\[ SE = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.85 \times 0.15}{175}} = \sqrt{\frac{0.1275}{175}} = \sqrt{0.000728571} \approx 0.027 \][/tex]
Test statistic (z):
[tex]\[ z = \frac{\hat{p} - p}{SE} = \frac{0.7714 - 0.85}{0.027} = \frac{-0.0786}{0.027} \approx -2.91 \][/tex]
5. Determine the p-value
Using the standard normal distribution, we find the p-value for [tex]\( z = -2.91 \).[/tex]
Looking up this value in a z-table or using a statistical calculator, the p-value for [tex]\( z = -2.91 \)[/tex] is approximately 0.0018.
6. Make a decision
Since the p-value (0.0018) is less than the significance level [tex]\( \alpha = 0.05 \)[/tex], we reject the null hypothesis.
There is statistical evidence at the 0.05 significance level to support the claim that the effectiveness of the medication is less than 85%.
simplify
x^1/3 ( x^1/2 + 2x^2 )
Answer:
x^5/6 + 2x^7/3.
Step-by-step explanation:
x^1/3 ( x^1/2 + 2x^2 )
= x^(1/3 + 1/2) + 2x^(1/3 + 2)
= x^5/6 + 2x^7/3
The simplified form of the expression [tex]x^{1/3} ( x^{1/2} + 2x^2 )[/tex] is [tex]x^{5/6}+2x^{7/3}[/tex].
The given expression is [tex]x^{1/3} ( x^{1/2} + 2x^2 )[/tex].
Distribute [tex]x^{1/3}[/tex] to the expression in parenthesis.
[tex]x^{1/3} . x^{1/2} + x^{1/3}.2x^2[/tex]
When the bases are same then the powers will be added.
[tex]x^{1/3+1/2}+2x^{2+1/3}[/tex]
Lets solve the powers by using LCM of the fractions:
[tex]x^{(2+3)/6}+2x^{7/3}[/tex]
Simplify the powers:
[tex]x^{5/6}+2x^{7/3}[/tex]
Hence, the simplified form of the expression [tex]x^{1/3} ( x^{1/2} + 2x^2 )[/tex] is [tex]x^{5/6}+2x^{7/3}[/tex].
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Is (2,2) in the solution set of y ≥ 9x - 8?
graph the solutions of the inequality on a number line. describe the solution to the inequality.p>4
In ΔGHI, the measure of ∠I=90°, HI = 3 feet, and IG = 2.3 feet. Find the measure of ∠H to the nearest degree.
Answer:
37
Step-by-step explanation:
Answer:
37
Step-by-step explanation:
37.476 = 37
The area of a triangular block is 36 square inches. If the base of the triangle is twice the height, how long is the base of the triangle?
Answer: height as h and base as 2h.
A = ½(b)(h). Substituting known facts gives 36 =½(2h)(h), which means that 36 = h2
and therefore h = 6 inches, height = 12 in.
Step-by-step explanation: I hope this helps :]
Final answer:
To determine the length of the base of the triangle with an area of 36 square inches and the base being twice the height, we use the area formula for a triangle (A = bh/2). After solving the equation, we find that the height is 6 inches and the base, being twice the height, is 12 inches.
Explanation:
The question asks to find the length of the base of a triangle given the area and a relationship between its base and height. We can use the formula for the area of a triangle, which is A = bh/2, where A is the area, b is the base, and h is the height of the triangle. Given the area of 36 square inches and the base being twice the height (b = 2h), we substitute into the area formula to solve for the base.
Plugging in the values, the equation becomes:
36 = (2h)h/2
Multiplying both sides by 2 to eliminate the fraction gives us:
72 = (2h)(h)
Which simplifies to:
72 = 2h^2
Dividing both sides by 2 gives us:
h^2 = 36
And taking the square root of both sides yields:
h = 6 inches
Knowing that the base is twice the height, we can find the base:
b = 2h = 2(6) = 12 inches
Therefore, the length of the base of the triangle is 12 inches.
PLEASE HELP
Find the surface area of a triangular prism, base measures 6 cm, height measures 4 m, sides measure 5 cm and height of prism measures 10 cm
Answer:
v=99.215674164922cm^2
Check all of the following that are proper units for measuring length in the
U.S. system of units.
A. Grams
B. Feet
C. Inches
D. Kilometers
Answer:
all except kilometers
Step-by-step explanation:
Select whether the equation has a solution or not
-roots
-no roots
help please guys!!!!
Answer:
they are like terms
Step-by-step explanation:
the sign ± is not a matter only veriable and power
In algebra, like terms are terms that have the same variables and powers. The coefficients do not need to match. Unlike terms are two or more terms that are not like terms, i.e. they do not have the same variables or powers. The order of the variables does not matter unless there is a power.
Identify the slope and y-intercept of the line given by the equation: y = 2x + 1.
Answer:
The slope is 2 and the y-intercept is 1 (hope this helped!)
Slope = 2, y-intercept = 1
What is intercept form of line?An intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept.
Given equation of line
y = 2x+1
comparing it with standard intercept equation of line
y = mx+c
where m is slope and c is the y-intercept.
Slope m = 2
Y- intercept c = 1
Hence, the slope and y- intercept of the line are 2 and 1 respectively.
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Find the best buy (based on price per unit) for cereal.
18-ounce size: $4.79
21-ounce size: $3.89
32-ounce size: $6.49
The best buy for cereal is the 21-ounce size as it costs $0.185 per ounce, which is cheaper compared to the 18-ounce size ($0.266 per ounce) and the 32-ounce size ($0.203 per ounce).
Explanation:To determine the best buy for cereal, we first need to calculate the price per ounce for each size. The formula to calculate is Price per Ounce = Total Price / Ounce Size. Using this formula, let's calculate for each cereal pack:
18-ounce size: $4.79/18 = $0.266 per ounce 21-ounce size: $3.89/21 = $0.185 per ounce 32-ounce size: $6.49/32 = $0.203 per ounce.
Based on these calculations, we see that the 21-ounce size cereal pack is the best buy, as it offers the lowest price per ounce.
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which expression has a value of 36 when x = 4 and y=7
Answer:84
Step-by-step explanation:you have to add 54 plus 3
Which set of measurements will form a unique triangle?
angle measures of 45°, 45°, 90°
angle measures of 60°, 60°, 60°
side measures of 1 cm, 1 cm, 100 cm
side measures of 20 cm, 20 cm, 20 cm
Answer:
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Take the first two numbers (60 and 60) and add them, then compare it to the last number (60). If the answer from adding is greater than the 3rd number, you have your answer :) Hope this helps!
Ryan plays basketball. Last year he averaged 22.8 points per game during his team’s 20 game
season. The schools record for total points scored in a season is 500 points. If Ryan increases his
scoring by 25%, will he break the school’s record? Show all work to support your conclusion.
Answer:
He would break the school record by 70 points.
Step-by-step explanation:
22.8*20= 456
456*.25= 114 (how many points he would be getting if he increased his scoring by 25%)
456+114= 570
The table shows the scores of 10 students in Mr. Garcia’s 3rd period math class on their last 20-point quiz.
Name Quiz Score
Kelsey 18
Adam 12
Matthew 15
Maria 10
Victoria 13
Michael 20
Jessica 16
Anna 12
Brandon 18
Luis 6
What is the absolute deviation of Victoria’s quiz score from the mean?
A. 0 points
B. 2 points
C. −1 point
D. 1 point
Please give an answer
Marty bought a shirt for $9.50, sandals for $15.50, shorts for $11.75, and sunscreen for $5.25. Use mental math to find the total amount he spent. Explain.
Answer:
42
Step-by-step explanation:
9.5+15.5=25. 11.75+5.25=17. 25+17=42. That should explain it. I hope this helps.
Answer:
Marty spent $42. How I got this answer is I added 11.75+5.25 first, equaling 17. Then I added 15.50 to 17, equaling 32.50. Finally I added 9.50 to 32.50 equaling 42.
Step-by-step explanation:
9.50+15.50+11.75+5.25= $42
A car race is 500 miles long. If each lap is 2 miles and 50 laps have already
been completed, how many more laps are left in the race?
laps
Answer:
200 laps left
Step-by-step explanation:
50 * 2 = 100
100 miles have been completed
500 - 100 = 400
400 miles left
400 / 2 = 200
200 laps left
. Which one of the following equals a negative
number?
A) (-5) +9
B) (-9) + 5
C) 9+ 5
D) 5+(-9) +4
F) 9-(-5)
Answer:
b
Step-by-step explanation:
looked it up
Answer:
i think its b
Sara goes shopping with $100 at the mall and she used th
calculate the amount of change she should receive. How
the end of the day?
100 - (12 + 17 + 7 + 2(4) + 3(5) + 4)
$37
$0
$42
$21
Answer:
$37
Step-by-step explanation:
2x4=8
3x5=15
12+17+7+8+15+4=63
100-63=37
$37
Answer:37
Step-by-step explanation: 12+17=29 29+7=36 36+8=44 44+15=59 59+4=63 And you 2(4) you multiply and 3(5) you also multiply
Then you subtract 100 and 63and get 37
A line passes through the points (–5, 2) and (10, –1). Which is the equation of the line?
y = negative one-fifth x + 1
y = one-fifth x + 3
y = –5x – 23
y = 5x + 27
Answer:
a. y = negative one-fifth x + 1
Step-by-step explanation:
The linear function of a line that passes through points (–5, 2) and (10, –1) will be y = (-1/5)x + 14.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given,
The line passes through points (–5, 2) and (10, –1)
Slope m = (-1 - 2)/(10 + 5)
Slope m = -3/15
m = -1/5
Thus, y = (-1/5)x + c
Put (10, –1)
-1 = (-1/5)10 + c
c = 14
Thus, the linear equation will be as, y = (-1/5)x + 14
Hence "The linear function of a line that passes through points (–5, 2) and (10, –1) will be y = (-1/5)x + 14.".
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I NEED HELP ASAP RIGHT NOW NOW NOW
Answer:
2^120
Step-by-step explanation:
6 x 20 = 120
Answer:
4²⁶
Step-by-step explanation:
It's easier than you think; all you need to do is multiply 2⁶ x 2²⁰.
Multiply the bases and add the exponents. You will get 4²⁶.
Tom invested £1000 for 2 years with Bettabank.
He got 2.5% simple interest each year.
Jay invested £1000 for 2 years with Moneyplus.
She got a total of £60 interest for the 2 years.
Show that Jay got the better investment.
Answer:
Since Tom got only £50 while Jay got £60 for th same amount invested in the same time, Jay got the better investment.
Step-by-step explanation:
In order to show that Jay got a better investment we first need to calculate how much Tom earnt in simple interest during those two years. In order to do that we must apply the correct formula shown below:
M = c*r*t
Where M is the total of interest, c is the amount invested, r is the rate of interest and t is the time elapsed. Thefore Tom got:
M = 1000*0.025*2
M = £50
Since Tom got only £50 while Jay got £60 for th same amount invested in the same time, Jay got the better investment.
Evaluate sin 5pi/4
Thank you
Answer:
-sqrt(2)/2
Step-by-step explanation:
5pi/4 lies in the third quadrant with basic angle: 5pi/4 - pi = pi/4
sin(pi/4) = sqrt(2)/2
Since it's in quadrant 3, sin would be negative
sin(5pi/4) = -sqrt(2)/2
sqrt: square root
When the above math expression is evaluated, the value of sin(5π/4) is -√2/2.
How is this so?
To evaluate sin(5π/4), we can use the unit circle or trigonometric identities.
The angle 5π/4 is located in the third quadrant of the unit circle, where the sine function is negative.
In the unit circle, at 5π/4, the corresponding point is (-√2/2, -√2/2). The y-coordinate of this point represents the value of the sine function.
Therefore, sin(5π/4) = -√2/2. hence, the value of sin(5π/4) is -√2/2.
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Give the equation of the line that passes through the points (4,6) and (-2,3)
A. y = 2x + 7
B. y = 1/2x + 7
C. y = 2x + 4
D. y = 1/2x + 4
Answer:
y = 1/2x+4
Step-by-step explanation:
First we find the slope
m = (y2-y1)/(x2-x1)
= (3-6)/(-2-4)
= -3/-6
=1/2
The equation of a line in slope intercept form is
y = mx+b where m is the slope and b is the y intercept
y =1/2x+b
Substitute one of the point into the equation
6 = 1/2(4) +b
6 = 2+b
b=4
y = 1/2x+4
Answer:
D. y = 1/2x + 4
Step-by-step explanation:
Slope: (6-3)/(4--2) = 3/6 = 1/2
y = ½x + c
6 = ½(4) + c
6 = 2 + c
c = 4
y = ½x + 4
I really need help with this question.
Answer:
I got 4/5
Step-by-step explanation:
In the equation, t is a constant. If the equation has no real solutions, what could be the value of t?
2x2 − 4x = t
A) −3
B) −1
C) 1
D) 3
Answer:
t = - 3
Step-by-step explanation:
2x2 - 4x = t
2x2 - 4x - t = 0
a = 2, b = - 4, c = - t
b2 - 4ac = 0
(-4) - 4(2)(-t) = 0
16 + 8t = 0
8t = - 16
t = - 3
good day, and be safe
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Mike thought of a number. He added to it to two other numbers. One of these numbers was 12 less than his number, the other was 12 more than his number. The result of the addition was 15. What was Mike’s original number?
If Mikes original number is x, the equation is?
The number is?
Answer:
number 1 + number 2 + number 3 = 15
Number 1 = x + 12
Number 2 = x - 12
Number 3 = x
(x + 12) + (x - 12) + x = 15
x + 12 + x - 12 + x = 15
x + x + x +12 -12 = 15
3x = 15
x = 15/3 = 5
Check:
Number 1 = 17
Number 2 = 5 -12 = -7
Number = 5
number 1 + number 2 + number 3 = 15
17 + (-7) + 5 = 15
10 + 5 = 15
15 = 15
Answer is 5
Step-by-step explanation:
A circle has the equation x2+y2−8x−2y−17=0.
What is the equation of the circle in standard form?
(x−4)2+(y−1)2=34
(x+4)2+(y−1)2=34
(x−4)2+(y−1)2=17
(x+4)2+(y−1)2=17
Answer:
A
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Given
x² + y² - 8x - 2y - 17 = 0
Collect the x- terms and the y- terms together and add 17 to both sides
x² - 8x + y² - 2y = 17
Use the method of completing the square on both x and y terms.
add ( half the coefficient of the x/ y terms )² to both sides
x² + 2(- 4)x + 16 + y² + 2(- 1)y + 1 = 17 + 16 + 1
(x - 4)² + (y - 1)² = 34 → A
Answer:
(x−4)2+(y−1)2=34
Step-by-step explanation: hope this helps :)