Answer:
y = -3x + 7
Step-by-step explanation:
a line perpendicular to y=1/3x + 2 must have a slope of -3 (the opposite reciprocal)
we can use slope (m) of -3 and the point (2,1) to write the equation:
y = mx + b
1 = (-3)(2) + b
1 = -6 + b
b = 7
Putting it all together you get:
y = -3x + 7
Convert 15meter to 5kilometer
Answer:
Step-by-step explanation:
1 m =0.001 km
15m=15*0.001
=0.015 km
A cable 27 feet long runs from the top of a utility pole to a point on the ground 16 feet from the base of the pole. How tall is the utility pole?
Answer:
15^2+x^2=22^2
225+x^2=484
x^2=259
x=16.09 feet
Step-by-step explanation: 15^2+x^2=22^2
225+x^2=484
x^2=259
x=16.09 feet
A survey of nonprofit organizations showed that online fundraising increased in the past year. Based on a random sample of 60 nonprofit organizations, the mean one-time gift donation in the past year was $75, with a standard deviation of $12. If you test the null hypothesis at the 0.05 level of significance, is there evidence that the mean one-time gift donation is greater than $70?
Answer:
The p-value of the test is 0.001 < 0.05, which means that there is evidence at the 0.05 level of significance that the mean one-time gift donation is greater than $70.
Step-by-step explanation:
Test if the mean one-time gift donation is greater than $70:
At the null hypothesis, we test if it is 70 or less, that is:
[tex]H_0: \mu \leq 70[/tex]
At the alternate hypothesis, we test if it is greater than 70, that is:
[tex]H_1: \mu > 70[/tex]
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.
70 is tested at the null hypothesis:
This means that [tex]\mu = 70[/tex]
Based on a random sample of 60 nonprofit organizations, the mean one-time gift donation in the past year was $75, with a standard deviation of $12.
This means that [tex]n = 60, X = 75, s = 12[/tex].
Test statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{75 - 70}{\frac{12}{\sqrt{60}}}[/tex]
[tex]t = 3.23[/tex]
P-value of the test:
The p-value of the test is the probability of finding a sample mean above 75, which is a right-tailed test with t = 3.23 and 60 - 1 = 59 degrees of freedom.
Using a t-distribution calculator, this p-value is of 0.001.
The p-value of the test is 0.001 < 0.05, which means that there is evidence at the 0.05 level of significance that the mean one-time gift donation is greater than $70.
solve for x:
x + 2 1/3 = 3 1/5
x-2 2/3 = 5/6
A cupcake recipe takes 3 cups of flour for every 2 dozen cupcakes. How many cups of flour does Sally need to make 96 cupcakes? Use the table to help.
Answer: 12 cups of flour
Step-by-step explanation:
12 cups of flour 3 + 3 + 3 + 3 = 12 because I have to make 96 cupcakes for tomorrow.
The amount of flour required will be 8 x 1.5 = 12 cups of flour. Option A is correct.
What is the Ratio?The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.
To make 2 dozen cupcakes, the recipe requires 3 cups of flour. Therefore, for 1 dozen cupcakes, the recipe requires 1.5 cups of flour (since 2 dozen cupcakes = 2 x 1.5 = 3 cups of flour).
To make 96 cupcakes, Sally needs 8 dozen cupcakes (since 8 x 12 = 96). Therefore, the amount of flour required will be 8 x 1.5 = 12 cups of flour.
So, the answer is 12 cups of flour, and the explanation should be:
To make 2 dozen cupcakes, the recipe requires 3 cups of flour. Therefore, for 1 dozen cupcakes, the recipe requires 1.5 cups of flour. To make 96 cupcakes, Sally needs 8 dozen cupcakes.
Therefore, the amount of flour required will be 8 x 1.5 = 12 cups of flour.
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f(x)=x^2-5 and g(x)=3x+1 then f(g(2))
Answer:
f(g(2)) = 44
Step-by-step explanation:
g(2) = 3(2) + 1 = 7
Plug 7 into f(x) since g(2) = 7
f(7) = 7² - 5 = 44
f(g(2)) = 44
Given P(A) = 0.3, P(B) 0.63 and P(BA) = 0.79, find the value of
P(A and B), rounding to the nearest thousandth, if necessary.
Answer:
P(A and B) = 0.14.
Step-by-step explanation:
Venn probabilities:
Suppose we have two events, A and B. The probability P(A and B) is given by:
[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B)[/tex]
In which [tex]P(A \cup B)[/tex] is P(A or B).
In this question:
P(A) = 0.3, P(B) = 0.63, P(A or B) = 0.79. So
[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B) = 0.3 + 0.63 - 0.79 = 0.93 - 0.79 = 0.14[/tex]
So
P(A and B) = 0.14.
Mary’s bedroom rug is shown below. Find the perimeter and area of the rug.
]This problem is for my math class
Solve the inequality below
6x - 5 < 55
Answer: x < 10
Step-by-step explanation: Just like any of your two-step equations, in this inequality, start by isolating the x term which in this case is 6x by adding 5 to both sides.
That leaves you with 6x < 60 and now just divide both sides by 2 and x < 10.
Notice that because we divide both sides of the inequality
by a positive number, not a negative, we did not change the
direction of the inequality sign.
Finally, put your answer in set notation, {x: x < 10}.
Unlike an equation which normally has one solution, the answer to an inequality must be stated as a solution set because an entire set of answers will work. In this problem, it's any number less than 10.
Analyze the diagram below and answer the the question that follows. Which statement is false? A. Angle MNO is congruent to angle OPM by SSS. B. angle MON is congruent to angle OMP by SAS. C. angle MPO is congruent to angle MNO by SAS. D. MO = OM
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Answer:
C. triangle MPO is congruent to triangle MNO by SAS
Step-by-step explanation:
Enough information is given in the diagram so that we know ...
ΔMNO ≅ ΔOPM
by either the SSS or SAS congruence postulates.
What makes statement C false is the fact that the vertices listed are not corresponding vertices.
_____
Additional comment
The wording here is of the form <angle 1> is congruent to <angle 2> by <some triangle congruence postulate>. A triangle congruence postulate can be used to show triangle congruence. Angle congruence must be based on a different claim.
Help plz:)))I’ll mark u Brainliest
Answer:
[tex]tan^{-1}(\frac{12}{16})[/tex] = 36.87°
≈37°
Question 20
Josh says that has the same quotient as Is this true or false?
O True
O False
A garden flower grows a total of 10 cm in July and August. Assuming that the flower grows at a consistent rate for a full year, how much will the flower grow in a year?
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Answer:
60 cm
Step-by-step explanation:
July and August are 2 of the 12 months in the year. The growth for the year can be expected to be 6 times the growth in a 2-month period, so 60 cm.
_____
You could get down to particulars as to the number of days in those two months versus the total number of days in a year. You would have to specify whether it is a leap year. In a non-leap year, the growth might be ...
365/(31+31) × 10 cm ≈ 58.9 cm
In a leap year, it would be 59.0 cm.
You have inherited land that was purchased for $25,000 in 1970. The value of the land has appreciated by
approximately 4% per year. What was the value of the land in the year 2000?
(a) Write the exponential function for this scenario:
(b) What was the value of the land in the year 2000? Round to the nearest whole dollar.
A. $750,000
B. $605,035,808
C. $81,084
D. $7,346
Answer:
Future value of land = 25,000[1.04]³⁰
Future value of land = $81,084 (Approx.)
Step-by-step explanation:
Given:
Purchase cost of land in 1970 = $25,000
Application rate = 4% per year
Find:
Price of land in 2000
Computation:
Number of year = 2000 - 1970 = 30 year
Future value of land = [Purchase cost of land][1+Application rate]ⁿ
F = P[1+r]ⁿ
Future value of land = 25,000[1+4%]³⁰
Future value of land = 25,000[1+0.04]³⁰
Future value of land = 25,000[1.04]³⁰
Future value of land = 25,000[3.24339]
Future value of land = 81,084.75
Future value of land = $81,084 (Approx.)
Calculate the surface area of the following object 8 km 14 km:
Which one you think is the correct answer?
1- 15834 km
2- 1926.0 km
3- 6597 km
4- 1935.2 km
Answer:
1.option is the correct answer right
HELP
Which equation has no real solution A. B2 + 3b = -3
B. 2c2 + 4c = 9
C. -5c2 – c= -2
D.7g +1 + 3g2 = 0
Answer:
A.
[tex] {b}^{2} + 3b - 3 = 0[/tex]
Step-by-step explanation:
[tex] {b}^{2} + 3b - 3 = 0 \\ because \: \: {b}^{2} < 4ac \\ {b}^{2} = {3}^{2} = 9 \\ 4ac = 4 \times 1 \times - 3 = - 12 \\ hence : {b}^{2} < 4ac[/tex]
PLEASE HELP ASAP Use the figure to complete the following trigonometric ratios.
Answer:
[tex]sinB=\frac{15}{17} , cos B=\frac{8}{17} , tanB=\frac{15}{8} \\sinA=\frac{8}{17} , cos A=\frac{15}{17} , tanA=\frac{8}{15}[/tex]
Step-by-step explanation:
[tex]sinB=\frac{15}{17} , cos B=\frac{8}{17} , tanB=\frac{15}{8} \\sinA=\frac{8}{17} , cos A=\frac{15}{17} , tanA=\frac{8}{15}[/tex]
Find the distance from the point (1,4) to the line y = 1/3x - 3.
A) 4 units
B) 20 units
C) 4 units
OD) 20 units
Answer:
answer
is 6.325.............
Answer:
2√10
Step-by-step explanation:
I also got this question and it says I got it correct with this answer choice
Please answer the ones you know or all of them
Answer:
solve each equation :
12) B) {0}
13)(B) {-3}
14) (C) {4}
If f(x)=5^x+2x and g(x)=3x-6
find (f+g)(x)
Answer:
(f+g)(x) = 5^x+5x-6
Step-by-step explanation:
f(x)=5^x+2x
g(x)=3x-6
(f+g)(x) = 5^x+2x+3x-6
Combine like terms
(f+g)(x) = 5^x+5x-6
A = 7x2 - 3x + 10
B = -4x2 + 6x - 4
A - B =
Your answer should be a polynomial in standard form.
Answer:
A - B = 11x² -9x + 14
A - B = 11x² -9x + 14
Keano and Emily are going to Europe to buy some shoes, they will need €1500. How many American Dollars will it take to get that much, knowing that the exchange rate of USD: EUR is €1: $1.14 *
Answer:
1710
Step-by-step explanation:
you will multiply 1500 euros by the exchange rate
Help me PLEASEEEEEEEEEEEEE
Answer:
Positive number: Elevation of a mountain above sea level, growth of a plant, money saved. Negative number: Temperature colder than 0.
Step-by-step explanation:
Elevation of a mountain that is above sea level is positive since it isn't below sea level, which would be negative, you are increasing as you go up. Growth of a plant is positive since it isn't growing shorter. Money saved since you aren't spending it. Temperature colder than 0 because that is when the negative numbers start to occur.
Answer:
Step-by-step explanation:
the first box goes in negative, second box in positive, third box in negative, and fourth box in positive.
* But for the first box i’m not completely sure, hope this helped.
Find the median and mean of the data set below:
25, 13, 6, 4,2
Answer: im sorry but there is nothing here to help? may you add a picture? or something file maybe?
Step-by-step explanation:
A box is filled with 2 red carts, 3 green cards, and 8 brown cards. A card is chosen at random from the box, What is the grobability that the card is not green?
Write your answer as a fraction in simplest form.
Answer:
10/13
Step-by-step explanation:
High. Very High
The total number of cards is 8 + 3 + 2 = 13
There are 3 green ones and 10 others.
P(~G) = 10/13 = 0.769
PLEASE HELP ME I BEG YOU
1- False
2- False
3- False
4-False
Find an equation for the perpendicular bisector of the line segment whose endpoints
(5, -3) and (-7, -7).
are
Answer:
[tex]y=-3x-8[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Midpoint: [tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex] where the endpoints are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)Perpendicular lines always have slopes that are negative reciprocals (ex. 2 and -1/2, 3/4 and -4/3, etc.)1) Determine the midpoint of the line segment
When two lines bisect each other, they intersect at the middle of each line, or the midpoint.
[tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex]
Plug in the endpoints (5, -3) and (-7, -7)
[tex](\frac{5+(-7)}{2} ,\frac{-3+(-7)}{2} )\\(\frac{-2}{2} ,\frac{-10}{2} )\\(-1,-5)[/tex]
Therefore, the midpoint of the line segment is (-1,-5).
2) Determine the slope of the line segment
Recall that the slopes of perpendicular lines are negative reciprocals. Doing this will help us determine the slope of the perpendicular bisector.
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] where the given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the endpoints (5, -3) and (-7, -7)
[tex]\frac{-7-(-3)}{-7-5}\\\frac{-7+3}{-7-5}\\\frac{-4}{-12}\\\frac{1}{3}[/tex]
Therefore, the slope of the line segment is [tex]\frac{1}{3}[/tex]. The negative reciprocal of [tex]\frac{1}{3}[/tex] is -3, so the slope of the perpendicular is -3. Plug this into [tex]y=mx+b[/tex]:
[tex]y=-3x+b[/tex]
3) Determine the y-intercept of the perpendicular bisector (b)
[tex]y=-3x+b[/tex]
Recall that the midpoint of the line segment is is (-1,-5), and that the perpendicular bisector passes through this point. Plug this point into [tex]y=-3x+b[/tex] and solve for b:
[tex]-5=-3(-1)+b\\-5=3+b[/tex]
Subtract 3 from both sides
[tex]-5-3=3+b-3\\-8=b[/tex]
Therefore, the y-intercept of the line is -8. Plug this back into [tex]y=-3x+b[/tex]:
[tex]y=-3x-8[/tex]
I hope this helps!
A town recently dismissed 88 employees in order to meet their new budget reductions. The town had 77 employees over 5050 years of age and 1717 under 5050. If the dismissed employees were selected at random, what is the probability that at least 66 employees were over 5050? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answer:
0.0013 probability that at least 6 employees were over 50.
Step-by-step explanation:
The employees were "chosen" to be dismissed without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem:
8 employees dismissed means that [tex]n = 8[/tex]
Had 7 + 17 = 24 employees, which means that [tex]N = 24[/tex]
7 over 50, which means that [tex]k = 7[/tex]
What is the probability that at least 6 employees were over 50?
6 or 7, so:
[tex]P(X \geq 6) = P(X = 6) + P(X = 7)[/tex].
In which
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 6) = h(6,24,8,7) = \frac{C_{7,6}*C_{17,2}}{C_{24,8}} = 0.0013[/tex]
[tex]P(X = 7) = h(7,24,8,7) = \frac{C_{7,7}*C_{17,1}}{C_{24,8}} \approx 0[/tex]
[tex]P(X \geq 6) = P(X = 6) + P(X = 7) = 0.0013 + 0 = 0.0013[/tex]
0.0013 probability that at least 6 employees were over 50.
Need some help on this
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Answer:
a. set 1: 29 minutes; set 2: 25 minutes
b. set 1 is more challenging than set 2
Step-by-step explanation:
a. The mean is found by adding the times and dividing by the number of times. For set 1, that is ...
(2×27 +2×28 +3×29 +2×30 +33)/10 = 290/10 = 29 . . . minutes
For set 2, that is ...
(4x24 +4×25 +2×27)/10 = 250/10 = 25 . . . minutes
__
b. The mean of set 1 is higher, and the spread is wider, suggesting more students have more trouble with the problems of set 1. That is, ...
set 1 is more challenging than set 2
Determine the slope of the line passing through (4, -2) and (7, 10).
Answer:
4
Step-by-step explanation:
To find slope without a graph, you subtract the 2 y-coords and the 2 x-coords, then divide the y-coord by the x-coord.
The formula is (y²-y¹)/(x²-x¹).
So we just plug in the coordinates.
(10-(-2))/(7-4)
(10+2)/(7-4)
12/3
4
So the slope is 4.
---
hope it helps
The slope of the line passing through (4, -2) and (7, 10) is,
⇒ m = 4
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
We have to given that;
Two points on the line are (4, -2) and (7, 10).
Since, The equation of line passes through the points (4, -2) and (7, 10).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (10 - (-2)) / (7 - 4)
m = 12 / 3
m = 4
Thus, The slope of line = 4
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