Answer:
b = 3
Step-by-step explanation:
All you need to do is subtract 3 from both sides, like so:
6 = 3 + b
-3 -3
________
3 = b
Answer:
B = 3
Step-by-step explanation:
6 = 3 + b, subtract the 3 from 6
6 - 3 = b
3 = b
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
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 :)
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].
To learn more on Expressions click:
https://brainly.com/question/14083225
#SPJ6
What is m<1 if m<3=80
Angles 1 and 3 are vertical angles, so they are congruent.
how do you expand (x-10)(x-10)
What is the area of figure ABCD?
104 square inches
120 square inches
136 square inches
168 square inches
Answer:
The answer is option 2.
Step-by-step explanation:
You have to use the formula of area of trapezium :
[tex]area = \frac{1}{2} \times (ab + cd) \times bc[/tex]
Let AB be 13 inches,
Let CD be 17 inches,
Let BC be 8 inches,
[tex]A = \frac{1}{2} \times (13 + 17) \times 8[/tex]
[tex] = \frac{1}{2} \times30 \times 8[/tex]
[tex] = \frac{1}{2} \times 240[/tex]
[tex] = 120 \: {inches}^{2} [/tex]
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
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
Is (2,2) in the solution set of y ≥ 9x - 8?
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
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
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.
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%.
Which pair of
expressions are
equivalent?
A. 8(2r) and 10r B. 6r + 3 and 9r
C. 9(3r-4) and 27r - 36
D. r+r+r+r+r and r^5
The pair of expressions that are equivalent are 6r + 3 and 9r, and 9(3r-4) and 27r - 36.
Let's simplify each expression to see which pairs are equivalent:
A. 8(2r) = 16rB. 6r + 3 = 9rC. 9(3r - 4) = 27r - 36D. r + r + r + r + r = r^5Now, let's compare them:
A. 16rB. 9rC. 27r - 36D. r^5The equivalent pairs are:
B. 6r + 3 and 9r (after simplification, both equal 9r)C. 9(3r - 4) and 27r - 36 (after simplification, both equal 27r - 36)So, the correct answer is:
B. 6r + 3 and 9r C. 9(3r-4) and 27r - 36
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 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.".
For more about the linear function,
brainly.com/question/21107621
#SPJ6
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
Read more about least square regression equation at:
https://brainly.com/question/17695497
The height and radius of a cylinder are 23cm and 5cm what the volume?
Answer:
Around 1806.42
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.
graph the solutions of the inequality on a number line. describe the solution to the inequality.p>4
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.
Learn more about intercept equation of line here:
https://brainly.com/question/9682526
#SPJ3
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.
3.43
Can you help me Simplify this question
Answer:
192
Step-by-step explanation:
3 * 4^3
Using PEMDAS
Exponents first
4^3 = 4*4*4 = 64
Replace into the expression
3 *64
3*64 =192
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.
Select whether the equation has a solution or not
-roots
-no roots
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
What is true about the points on the graph of y=2x?
A. Two of the coordinates on the graph are solutions to the equation y=2x.
B. There is one coordinate on the graph that makes y=2x true.
C. As the x-coordinates increase by 1, the y-coordinates increase by 2.
D. You can substitute the x-coordinate into the expression 2x to get the y-coordinate.
The correct statements about the graph of the equation y=2x are that as the x-coordinates increase by 1, the y-coordinates increase by 2, and you can get the y-coordinate by substituting the x-coordinate into 2x.
Explanation:Concerning the equation y=2x, option C is the correct statement about the graph. This is because linear equations like this represent a direct proportionality between variables x and y. When the x-coordinate increases by 1, the y-coordinate increases by the coefficient of x, in this case, 2, reflecting the equation's slope which is the constant rate of change for y in relation to x. Option D is also true because, for any point on the graph, substituting the x-coordinate into the expression 2x will yield the corresponding y-coordinate, as per the definition of a functional relationship in algebra. Thus, solutions to the equation y=2x include an infinite number of points on the graph, not just two as stated in option A, making options A and B incorrect.
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.
Learn more about Price per Ounce here:https://brainly.com/question/32147222
#SPJ2
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
. 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