Answer:
A. y=-1/3x+10
Step-by-step explanation:
Perpendicular gradients(slopes) are negative reciprocals so
m=-1/3 then use the point (6,8) to find the equation of the line
y=mx+b
8=(-1/3)(6)+b
8=-2+b
b=10
y=-1/3x+10
⦁ A $10,000 certificate of deposit earns simple interest of 8 percent per year. Calculate the total earned money over the 5 year period?
Answer:
The total earned money over the 5 year period=$14,000
Step-by-step explanation:
We are given that
Principle amount, P=$10000
Rate of interest, r=8%
Time, t=5 years
We have to find the total earned money over the 5 year period.
We know that
Simple interest=[tex]\frac{P\times r\times t}{100}[/tex]
Using the formula
S.I=[tex]\frac{10000\times 8\times 5}{100}{/tex]
S.I=$4000
Now,
Amount=P+S.I
Amount=10000+4000
Amount=$14000
Hence, the total earned money over the 5 year period=$14000
1. How far is KFC from RCBC Savings Bank? 2. How far is BaliwagLetchon Manok from RCBC Savings Bank? 3. How far is Baliwag Lechon from his residence? 4. How far is KFC from his residence? 5. What is the measure of angle ERK ?
Answer:
Following are the solution to the given question.
Step-by-step explanation:
Please find the graph file and its solution in the attachment.
[tex]4x-15=3x+28\\\\4x-3x=28+15\\\\x=43\\\\[/tex]
Similarly:
[tex]3y+5=2y+50\\\\3y-2y=-5+50\\\\y=45\\\\[/tex]
For point 1:[tex]\to KR=4x-15= 4\times 43-15=172-15=157[/tex]
For point 2: [tex]\to BR=2y+50= 2\times 43+50=86+50=136[/tex]
For point 3:[tex]\to BE=KR=157[/tex]
For point 4:[tex]\to Kf=BR=130[/tex]
For point 5:[tex]\to ERK=KFB=180^{\circ} -\angle B-\angle ERB = 180^{\circ}-92^{\circ}-18^{\circ}=70^{\circ}[/tex]
Given that ΔKER and ΔBRE are congruent triangles, therefore:
1. How far KFC is from RCBC = KR = 157 m
2. How far BaliwagLetchon Manok is from RCBC Savings Bank = BR = 140 m
3. How far Baliwag Lechon is from his residence = BE = KR = 157 m
4. How far KFC is from his residence = KE = BR = 140 m
5. The measure of ∠ERK = 70°
What are Congruent Triangles?Congruent triangles have corresponding parts hat are congruent to each other.
Thus, given that ΔKER ≅ ΔBRE, find the values of x and y as shown below:
KR = BE
4x - 15 = 3x + 28
4x - 3x = 15 + 28
x = 43
KE = BR
3y + 5 = 2y + 50
3y - 2y = -5 + 50
y = 45
Thus:
1. How far KFC is from RCBC = KR
KR = 4x - 15
Plug in the value of x
KR = 4(43) - 15
KR = 157 m
2. How far BaliwagLetchon Manok is from RCBC Savings Bank = BR
BR = 2y + 50
Plug in the value of y
BR = 2(45) + 50
BR = 140 m
3. How far Baliwag Lechon is from his residence = BE = KR = 157 m
4. How far KFC is from his residence = KE = BR = 140 m
5. The measure of ∠ERK = 180 - (92 + 18) = 70°
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Pls I need help ASAP rn
Answer:
A) 48
Step-by-step explanation:
Given:
b = 16
c = 20
Pythagorean thm:
a² + b² = c²
a² + 16² = 20²
a² + 256 = 400
a² = 144
a = 12
To find perimeter:
P = a + b + c
P = 12 + 16 + 20
P = 48
A survey that asked people in the United States about their
feelings of personal well-being found that 85% are generally
happy. To test this finding, you survey 26 people at random and
finding that 19 consider themselves generally happy. Would
you reject the survey's findings?
Answer:
Yes I would
Step-by-step explanation:
You would not have enough test subjects to have an accurate survey.
Given a cylinder with a radius of 6 cm and a height of 12 cm, find the volume of the cylinder. Use 3.14 for \pi
Answer:
[tex]volume = \pi {r}^{2} h \\ = 3.14 \times {6}^{2} \times 12 \\ = 1356.48 \: {cm}^{3} [/tex]
Find the slope of the line tangent to the function y=6-3x at the point (5,0)
Answer:
-3
Step-by-step explanation:
To get the slope of the line tangent to the function y = 6 - 3x
First, we need to differentiate;
dy/dx = 0 -3x^{1-1}
dy/dx = 0 - 3x^0
dy/dx = 0 - 3
dy/dx = -3
Hence the slope of the line tangent to the function at the point is -3
Find the values of the variables in each figure.
Answer:
x = 40
Step-by-step explanation:
2x = 4x - 40 (recall properties of a parallelogram)
Solve for x
2x - 4x = 4x - 40 - 4x (subtraction property of equality)
-2x = -40
-2x/-2 = -40/-2 (division property of equality)
x = 20
help will give brainliest
Answer:
25 -2
Step-by-step explanation:
Suppose that the number of gallons of milk sold per day at a local supermarket are normally distributed with mean and standard deviation of 486.9 and 24.01, respectively. What is the probability that on a given day the supermarket will sell between 477 and 525 gallons of milk
Answer:
0.6032 = 60.32% probability that on a given day the supermarket will sell between 477 and 525 gallons of milk
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean and standard deviation of 486.9 and 24.01, respectively.
This means that [tex]\mu = 486.9, \sigma = 24.01[/tex]
What is the probability that on a given day the supermarket will sell between 477 and 525 gallons of milk?
This is the p-value of Z when X = 525 subtracted by the p-value of Z when X = 477.
X = 525
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{525 - 486.9}{24.01}[/tex]
[tex]Z = 1.59[/tex]
[tex]Z = 1.59[/tex] has a p-value of 0.9441
X = 477
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{477 - 486.9}{24.01}[/tex]
[tex]Z = -0.41[/tex]
[tex]Z = -0.41[/tex] has a p-value of 0.3409
0.9441 - 0.3409 = 0.6032
0.6032 = 60.32% probability that on a given day the supermarket will sell between 477 and 525 gallons of milk
Solve for x: 4/x - x/8 = 0
Answer:
[tex]x = \sqrt{32}[/tex]
Step-by-step explanation:
[tex]\frac{4}{x} - \frac{x}{8} = 0\\\\\frac{4}{x} = \frac{x}{8}\\\\x^2 = 32\\\\x = \sqrt{32}[/tex]
If you sleep 6 hours a day every day for a year you are sleeping of every year. If there are 365 days in a year, how
many days per year would you sleep? Simplify your answer and write it as a mixed number.
days
Answer:
Step-by-step explanation:
365 x 24 = 8,760
365 x 6 = 2,190
8,760 - 2,190 = 6,570
6,570 / 24 = 273 3/4
The person sleeps 91 (1/4) days per year.
What is multiplication?Multiplication is the process of adding a number up to a given number.
Given that, the person sleeps 6 hours a day.
The total hours of sleeping over a year are:
365 × 6
= 2190 hours per year
Since there are 24 hours in a day, divide 2190 by 24 to get the answer in days per hour:
2190/24
= 91 (1/4)
Hence, the person sleeps 91 (1/4) days per year.
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Use a 10-by-10 grid to model the percent.
1. 43%
Answer:
I diminished the amount that
Step-by-step explanation:
The difference in the x-coordinates of two points is 3, and the difference in the y-coordinates of the two points is 6. What is the slope of the line that passes through the points?
Answer:
2
Step-by-step explanation:
Slope is the ratio (quotient) of vertical change (the change in y) and the horizontal change (the change in x).
You may have heard "rise over run" as a phrase to help remember.
[tex]\frac{6}{3}=2[/tex]
Scores on Ms. Bond's test have a mean of 70 and a standard deviation of 11. Michelle has a score of 48. Convert Michelle's score to a z-score. (Round to two decimal places if necessary.)
Answer:
-2.00
Step-by-step explanation:
Applying,
Z = (x-μ)/σ.................. Equation 1
Where Z = Michelle z-score, x = Michelle score, μ = mean of the score, σ = Standard deviation of the score.
From the question,
Given: x = 48, μ = 70, σ = 11
Substitute these values into equation 1
Z = (48-70)/11
Z = -22/11
Z = -2.00
Hence Michelle's z-score is -2.00
A ladder 15 feet long leans against a wall making a 71 degree angle with the ground. How far from the base of the wall is the bottom of the ladder?
1. 14.18 feet
2. 4.88 feet
3. 15.86 feet
4. 9.38 feet
Answer:
2. 4.88 feet
Step-by-step explanation:
cos∅ = adj/hyp
cos71 = adj/15
adj = 15*cos71
adj = 4.88
What is Limit of (x cubed + 3 x squared minus 5) as x approaches negative 2?
–25
–15
–9
–1
Answer:
–1
Step-by-step explanation:
We want to find the following limit:
[tex]\lim_{x \rightarrow -2} x^3 + 3x^2 - 5[/tex]
Since the function does not have any discontinuity(point in which the denominator is 0, for example), we just replace the values of x by -2. So
[tex]\lim_{x \rightarrow -2} x^3 + 3x^2 - 5 = (-2)^3 + 3(-2)^2 - 5 = -8 + 12 - 5 = -13 + 12 = -1[/tex]
The value of the limit is -1.
Answer:
Step-by-step explanation:
D. -1
Solve the system of equations by graphing. {y=x+1
y=2x
Answer:
x=1, y=2
Step-by-step explanation:
There are 37 students who play a woodwind instrument in the school band. Of these, 7 play the saxophone. What percent of these students play the saxophone? Round to the nearest whole percent.
Answer:
19%
Step-by-step explanation:
A 4-story parking garage
has spaces for 240 + 285 + 250 + 267
cars. While one floor is closed for
repairs, the garage has spaces for
240 +250 + 267 cars. How many spaces
are there on the floor that is closed?
Explain.
the distance around the outside of a park is 0.6 mile. Elle biked 0.9 of the distance during her weekend. How far did she bike?
Multiply the total distance by the portion she rode:
0.6 miles x 0.9 = 0.54 miles
She rode 0.54 miles
Graph the solution to this system of inequalities in the coordinate plane. y > 1/4x + 6 y>2x - 4
Answer:
WVAD
Step-by-step explanation:
wdvvvvavdv
What are the main properties of a parallelogram?
use the parallelogram (ABEF) to help you
Answer:
It must be number 2.
1 and 3 number is wrong as parallelogram don't need have right angle
write the ratio of the garden's actual length to its length in the drawing. Use the variable x to represent the unknown measurement
The area of a rectangle is given by 3x3+14x2−23x+6. The width of the rectangle is given by x + 6. Find an expression for the length of the rectangle.
Answer:
is that 3x or mutiply sign
Answer:
3x^2-4x+1
Step-by-step explanation:
Evaluate arccos (-1/2)
Answer:
120 degrees
Step-by-step explanation:
plugged into calculator
cos inverse of -1/2
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Mindscapes: 11, 14, 16
Identify the vertex by completing the square: f(x) = x2 - 6x +8
Answer:
(3,-1)
Step-by-step explanation:
f(x)=(x2 - 6x)+8
f(x) = (x2 - 6x +9) + 8 - 9
f(x) = (x2 - 6x + 9) - 1
f(x) = (x - 3)^2 - 1
Since the completing square formula = a(x - h) + k
The vertex = (h,k)
= (3,-1)
write each verbal phrase as an algebraic expression.
1. the sum of 8 and t
2. the quotient of g and 15
3. the product of 5 and b
4. the difference of 32 and x
Answer:
1. 8 + t
2. g/15
3. 5b
4. 32 - x
Step-by-step explanation:
1. the sum of 8 and t
8 + t
2. the quotient of g and 15
g/15
3. the product of 5 and b
5b
4. the difference of 32 and x
32 - x
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Answer:
V = 30 cubic inches
Step-by-step explanation:
Given:
height (h) = 10 in.
Base area (B) = 9 in.²
Required:
Volume of the pyramid
Solution:
Formula for finding volume of triangular pyramid = ⅓(B)(h)
Plug in the values
V = ⅓(9)(10)
V = (3)(10)
V = 30 cubic inches