Answer:
Let x = smaller number and
y = larger number.
x + y = 42
x + 4y = 147
----------------
3y = 105
y = 35, so x = 7
The numbers are 7 and 35.
7 + 4(35) = 7 + 140 = 147
A proportional relationship is represented by the equation 4y = 24x. If y = kx, where k is the constant of proportionality what is the value of k? Show your work.
Please provide answer with explanation!!
Answer: k=6
Step-by-step explanation:
4y=24x Divide both sides by 4
y=6x
y=kx you can see k=6
but if they want you to actually prove
substitue y=6x into y=kx
you get
6x=kx divide both sides by x
6=k
someone please help me on rhis
The graph of a function g is shown below. Find g(1).
Check the picture below.
A woman was shot from a bullet that came through her front car window as she was driving through a business campus. Witnesses saw a muzzle flash from one of the office buildings but were not sure what floor it came from. The car was 40 feet from the building. The bullet hole in the window is 4 feet from the ground. Investigators were able to determine that the angle the bullet entered the glass was 2 degrees. Calculate how high off the ground the shot was fired.
The height of the shooter is 1.4 feet off the ground.
How to solve for the height of the shooterWe need to apply trigonometry. Our best choice will be to use the tangent function, which relates the opposite side (height of the shooter) to the adjacent side (distance from the shooter to the car), using the angle of elevation (2 degrees).
Let h = height of the shooter. Then, we can write:
tangent(2°) = h / 40
We can solve for "h" by multiplying both sides by 40 feet:
h = 40 * tangent(2°)
Using a calculator, we find that:
tangent(2°) = 0.0349
So, we have:
h = 40 * 0.0349
h = 1.396 feet
Therefore, the height of the shooter was approximately 1.4 feet (or 16.8 inches) off the ground.
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what is the ratio of perimeter to side length 6:7:10
If triangle has a perimeter of 69 cm, and ratio of side length as 6:7:10, then lengths of sides of triangle are 18 cm, 21 cm, and 30 cm.
The side length of the triangle are in the ratio = 6:7:10,
So, We let the lengths of the sides of the triangle be 6x, 7x, and 10x, where x is a constant.
Since the perimeter of the triangle is 69 cm, we have:
6x + 7x + 10x = 69
Simplifying the equation,
We get;
23x = 69
x = 3
So, the measure of sides of triangle are:
6x = 6×(3) = 18 cm
7x = 7×(3) = 21 cm
10x = 10×(3) = 30 cm
Therefore, the lengths of the sides are 18 cm, 21 cm, and 30 cm.
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The given question is incomplete, the complete question is
The lengths of the sides of a triangle are in the extended ratio 6 : 7 : 10. The perimeter of the triangle is 69 cm. What are the lengths of the sides?
Choose the inequality that represents this graph. Open circle at -5 open circle at 4, and shaded between -5 and 4
Answer:
The inequality is -5 < x < 4.
Maurice is traveling to Mexico and needs to exchange $370 into Mexico pesos. If each dollar is worth 12.29 pesos. How many peso will he get for his trip ?
Answer: 4547.30 pesos
Step-by-step explanation:
You can set up proportion
[tex]\frac{x}{370}=\frac{12.29}{1}[/tex] as long as you put pesos on top and dollars on bottom to set up proportion
now solve for x
x=12.29(370)= 4547.30 pesos
or
you can think of it as if you have 1 dollar and that is 12.29 pesos then 370 dollars would be 370x12.29
=4547.30
There are figures on the territory of a country in 2021 as follows:
Government spending on goods and services
Income from export factor 400
Import factor income 250
Export850
Imported 490
Net Investment: 350
Depreciation:520
Profit: 780
Salary:1700
Profit: 320
Household Consumption:2100
Indirect Tax 240
Rent530
Price index in 2021 is 135 and 2020 is 120
a. Calculate nominal GDP at market prices using the methods
b. Calculate GNP at market price and at factor cost
c. Calculate real GDP, real GNP and inflation rate in 2021
d. Calculate the economic growth rate in 2021 knowing the nominal GDP in 2020 is 3500.
Use the vertical line test to determine which graph does not represent a function. 0 Graph A M 10000 6 of 10 Graph B 0 Done
The graph that does not represent a function is graph b
Determine which graph does not represent a functionFrom the question, we have the following parameters that can be used in our computation:
Graphs A to C
As a general rule of the vertical line test
For a graph to represent a function, a line drawn from the x-axis must intersect with the graph at most once
using the above as a guide, we have the following:
The graph b would intersect with a line from the x-axis twice
Hence, the graph is b
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Mr. Johnson was paid $190 for a job that required 40 hours of work. At this rate, how much should he be paid for a job requiring 60 hours of work?
Answer:
Mr. Johnson should be paid $285 for a job requiring 60 hours of work.
Step-by-step explanation:
If Mr. Johnson was paid $190 for 40 hours of work, then we can write:
190/40 = x/60
Where x is the amount he should be paid for 60 hours of work.
To solve for x, we can cross-multiply and simplify:
190 * 60 = 40 * x
11,400 = 40x
x = 11,400/40
x = 285
Therefore, Mr. Johnson should be paid $285 for a job requiring 60 hours of work at the same rate.
What is the product? 1/2 . [12 64 78 30 ]
Answer:
[tex]\left[\begin{array}{c c c c}6 & 32 & 39 & 15\end{array}\right][/tex]
Step-by-step explanation:
When multiplying a constant by a matrix, we have to multiply each element by the constant.
[tex]\dfrac{1}{2} \cdot \left[\begin{array}{c c c c}12 & 64 & 78 & 30\end{array}\right][/tex]
[tex]= \left[\begin{array}{c c c c} \dfrac{12}{2} & \dfrac{64}{2} & \dfrac{78}{2} & \dfrac{30}{2}\end{array}\right][/tex]
[tex]= \left[\begin{array}{c c c c}6 & 32 & 39 & 15\end{array}\right][/tex]
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
x² + (y - 3)² = 36; x² + (y + 8)² =36 represent the circles that have a diameter of 12 units and a center that lies on the Y axis.
We know that the abscissa of coordinates of a point on Y axis is 0.
So the equation of a circle center at (0, k) and radius 'r' is given by,
x² + (y - k)² = r²
Here given that the diameter of the circle must be = 12 units
So the radius of the circle = 12/2 = 6 units.
So the equation of the required circle looks like
x² + (y - k)² = 6², where k is an real number.
x² + (y - k)² = 36
So we can see that the equations x² + (y - 3)² = 36; x² + (y + 8)² =36 can be the equation of the required circle.
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URGENT which expression is equivalent?
The equivalent expression to the given one is the second option:
[tex]log_2( y^4*z^4/x^2)[/tex]
Which expression is equivalent?Here you need to remember two logarithmic rules, these are:
[tex]log(x^n) = n*log(x)[/tex]
[tex]log(x) + log(y) = log(x*y)[/tex]
And these work for any base of the logarithm.
Here we start with the expression:
[tex]-2log_2(x) + 4log_2(y)+ 4log_2(z)[/tex]
Using the first one:
[tex]-log_2(x^2) + log_2(y^4) + log_2(z^4)[/tex]
Using the second one:
[tex]log_2( y^4*z^4/x^2)[/tex]
That is the equivalent expression, the second option.
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HELP PLEASE DUE IN A FEW
The values of b and c such that y = -11x² + bx + c has vertex (0,8) are given as follows:
b = 0.c = 8.How to obtain the vertex of a quadratic function?The standard definition of a quadratic function is given as follows:
y = ax² + bx + c.
The x-coordinate of the vertex is given as follows:
x = -b/2a.
For this problem, we have that a = -11, and we want a x-coordinate of 0 for the vertex, hence the value of b is given as follows:
b/22 = 0
b = 0.
At the x-coordinate of 0, y assumes a numeric value of 8, hence the value of c is given as follows:
-11(0)² + c = 8
c = 8.
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pls solve
-2n+1<5
pls explain solution
Answer:
n > -2
Step-by-step explanation:
[tex]-2n+1 < 5[/tex]
This is a two-step equation, so the first thing you would do is subtract 1 from both sides of the equation.
[tex]-2n+1-1 < 5-1\\-2n < 4[/tex]
Then, divide -2 from both sides of the equation.
[tex]\frac{-2n}{-2} < \frac{4}{-2} \\[/tex]
The less than symbol will become a greater than symbol because you divided by a negative number.
So the solution is:
[tex]n > -2[/tex]
Question 8 of 10
If two cylinders are similar and the ratio between the lengths of their edges is
4:3, what is the ratio of their volumes?
A 4:3
OB. 16.9
OC. 64.27
OD. 16:27
OD. 16.27
cylinder 4:3 the ratio if their volumes is (4/3)^3, which simplies to 64/27.So the correct answers is D.
You are writing a program to help compare two sports teams. A sample member of the list scores is [2.5] where
your team scored 2 and the opponent team scored 5. This part of the program is counting the wins and losses.
What is the missing line of code?
for item in scores:
sum sum + item[1]
if item[0]> item[1]:
Mark this and return
Save and Exit
TIVE REMAINS
59:11
Next
Submit answer
Here is the missing line of code is
if item[0] > item[1]:
wins += 1
else:
losses += 1
What is the complete code?The comlete code should look like this:
scores = [[2, 5], [3, 1], [4, 4], [1, 0], [2, 3] ]
wins = 0
losses = 0
for item in scores:
if item [0] > item[1] :
wins += 1
else:
losses += 1
print("Number of wins:", wins)
print("Number of losses:", losses)
This code examines the scores of the two teams for each game, and if the home team's score ( item [0]) is higher than the opponent team's score (item[1 ]), it counts as a victory, and the "wins" variable is increased by one.
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The table below shows the number of grams of fat contained in a pizza according to the number of meat toppings on the pizza.
Which equation best models this set of data?
Answer:
Plot the points on the graphing calculator, and then generate the best regression model. That model is:
F = 16.65x + 15.7
The closest equation is D.
A call center claims that the mean wait time for a customer to connect with a customer care executive is at most 2 minutes. A random sample of 20 calls at the call center yielded a test statistic of 1.75. Assuming that the wait time is normally distributed, what is the corresponding p-value? Round your answer to three decimal places.
Answer:
To find the p-value, we need to first find the corresponding area in the normal distribution table for the test statistic of 1.75.
Since the sample size (n) is greater than 30 and the population standard deviation is unknown, we use the t-distribution to calculate the p-value.
The degrees of freedom (df) for the t-distribution is n - 1 = 20 - 1 = 19.
Using a t-table or calculator, we can find that the area to the right of 1.75 (with df=19) is approximately 0.049.
Since this is a one-tailed test (the alternative hypothesis is that the mean wait time is greater than 2 minutes), the p-value is equal to the area to the right of the test statistic, which is 0.049.
Therefore, the corresponding p-value is 0.049 (rounded to three decimal places).
Step-by-step explanation:
gg
Find the value of x for the following
Applying the principle of similar triangles, the value of x is 6 units
What is similar trianglesSimilar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
To find the value of x in this problem, we have to apply similar triangle theorem here.
(8 + x) / 2√21 = 2√21 / x
cross multiply both sides
x(8 + x) = (2√21)(2√21)
8x + x² = 84
Rewrite the equation;
x² + 8x - 84 = 0
solving for x
x = 6, x= -14
Taking the positive value, the value of x = 6
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Tanya's garden measures 18 feet by 20 feet and has a perimeter of
76 feet. Marely's garden measures 12 feet by 33 feet.
How much longer is the perimeter of Marely's garden than Tanya's?
Answer:
I'm pretty sure the answer is 14 feet. hope this helps!
You want $500,000 in your account when you retire in 40 years. The account earns 11% interest. How much do you need to deposit each month to reach your goal?
I need to deposit $5,040.06 each month to reach my goal.
How to calculate the monthly deposit needed to reach your retirement goal?
To calculate the monthly deposit needed to reach your retirement goal, we can use the formula for the present value of an annuity, which is [tex]PMT \times [ \frac{(1 - (1 + r)^{-n})}{r} ] = PV[/tex]
where,
PMT is the monthly payment, r is the interest rate per month (11%/12 = 0.92%), n is the number of months (40 years x 12 months/year = 480 months) and PV is the present value of the annuity (which is my retirement goal of $500,000).
Plugging in the numbers,
[tex]PMT \times [ \frac{(1 - (1 + 0.0092)^{-480}) }{0.0092} ] = 500,000[/tex]
Solving for PMT,
PMT = $500,000 / [(1 - (1 + 0.0092)^(-480)) / 0.0092]
PMT = $500,000 / 99.17
PMT = $5,040.06
Therefore, to reach my retirement goal, you need to deposit $5,040.06 each month for the next 40 years.
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You need to deposit $73.06 each month to reach your goal of $500,000 at retirement at 11% interest.
What is simple and compound interest?Two different methods of calculating interest are used in finance: simple interest and compound interest.
Only the initial sum of money borrowed or invested, known as the principal, is used to calculate simple interest. The interest gained or charged is the same each period, and the interest rate is applied to the principal amount for a specific amount of time.
Contrarily, compound interest is determined by taking into account both the original principal as well as any prior interest payments. Each period's interest is combined with the principal, and the resulting sum serves as the foundation for calculating interest in the subsequent month.
The future value of the annuity is calculated using the formula:
[tex]FV = P * (((1 + r)^n - 1) / r)[/tex]
Thus, substituting the values we have:
[tex]500,000 = P * (((1 + 0.00917)^{480 }- 1) / 0.00917)[/tex]
Now,
[tex]P = 500,000 / (((1 + 0.00917)^{480} - 1) / 0.00917)[/tex]
P = $73.06
Hence, you need to deposit $73.06 each month to reach your goal of $500,000 at retirement.
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The cost of 3 sweaters and 2 pairs of jeans is $112.48. Two sweaters and one pair of jeans is
$65.10. Find the cost of each.
Hillary was told that based on the price of her home, her approximated closing costs would range from $11,600 to $40,600. How much was the price of her home?
We need more information about the property and the specific services required to determine the price of Hillary's home.
Answer:
Unfortunately, without additional information, it is impossible to determine the price of Hillary's home. The range of closing costs provided does not provide enough information to calculate the price of the home.
To determine the price of the home, we would need to know either the exact amount of the closing costs or additional information about the home's value, such as its appraised value or sale price.
Therefore, we cannot determine the price of Hillary's home based on the given information.
Step-by-step explanation:
We only know that the estimated closing costs for her home range from $11,600 to $40,600. Closing costs can vary based on a variety of factors, such as the location of the home, the type of mortgage, and the specific fees charged by the lender and other parties involved in the transaction.
To determine the price of Hillary's home, we would need additional information, such as the appraised value of the home, the amount of the down payment, and the specific closing costs that were incurred.
Giving a test to a group of students, the grades and gender are summarized below
Grades and Gender
A B C Total
Male 14 20 2 36
Female 15 19 18 52
Total 29 39 20 88
If one student is chosen at random, find the probability that the student was male AND got a "C". Round your answer to 4 decimal places.
The probability that the student chosen at random is male AND got a "C" is 0.0227.
What is Conditional Probability:Conditional probability is the probability of an event (A) occurring given that another event (B) has already occurred. It is denoted by P(A | B) and is read as "the probability of A given B".
The formula for conditional probability is:
P(A | B) = P(A and B) / P(B)
Where P(A and B) is the probability of both events A and B occurring, and P(B) is the probability of event B occurring.
Here we have
The total number of students is 88
Out of these 88 students, 36 are male
Number of males that got grade C = 2
P(male AND C) = number of males who got C / total number of students
= 2/88 = 0.02272727272
Rounding this to 4 decimal places, we get:
P(male AND C) = 0.0227
Therefore
The probability that the student chosen at random is male AND got a "C" is 0.0227.
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Find the quotient and remainder using long division for
x³ + 3x² + 6x + 10
x + 2
The quotient is
The remainder is
The quotient is x² + x + 4, and the remainder is 2.
x³ + 3x² + 6x + 10 = (x² + x + 4)(x + 2) + 2.
We have,
We can use long division to divide x³ + 3x² + 6x + 10 by x + 2:
x² + x + 4
------------------
x + 2 | x³ + 3x² + 6x + 10
- x³ + 2x²
--------
x² + 6x
- x² - 2x
---------
4x + 10
- 4x - 8
---------
2
Therefore,
The quotient is x² + x + 4, and the remainder is 2.
x³ + 3x² + 6x + 10 = (x² + x + 4)(x + 2) + 2.
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My watch gains 2 minutes in every 24 hours. If I put it right at 10 a.m. on Monday, what time will it show at 10 p.m. the same night? What time will it show at 10 a.m. on Tuesday? What time will it show at 10 a.m. on Wednesday? What time will it show at 10 a.m. on the following Monday?
The time your watch will show at 10 a.m. on the following Monday is 10:14 a.m.
What time will the watch show?If your watch gains 2 minutes in every 24 hours, that means it gains 1 minute every 12 hours.
At 10 a.m. on the following Monday (7 days after 10 a.m. on Monday):
7 days = 168 hours
12 hours = 1 minute
168 hours = ?
= 168/12
= 14 minutes
Your watch would show 10:14 a.m. on the following Monday, as it gains 1 minute every 12 hours and there are 7 days (168 hours) between Monday 10 a.m. and the following Monday 10 a.m.
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Question 3 of 10
What is the center of the circle shown below?
S
M
Ο A. A
B. AS
C. M
D. S
SUBMIT
The center of the circle shown is point S
Identfying the center of the circle shown?From the question, we have the following parameters that can be used in our computation:
The circle
By definition, the center of a circle is the point that is equidistant to all points on the circumference of the cirlce
In the given circle, the point that satisfies the above definition is the point S
This means that the circle can also be called the circle S
Hence, the center of the circle shown is S
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For this problem you need to determine the correct height of a flagpole large enough to support the Star Spangled Banner flag that flies over Fort McHenry. This flag is 30 by 42 feet in size. (We know that the ratio of the height of a flagpole to the width of any flag is 4 to 1.)
a. How tall will the flagpole need to be to support the Star Spangled Banner?
b. You have a model of Ft. McHenry that you need to add a flagpole to that would be proportional to the real pole at the fort. The ratio of the model is 1 inch to 10 feet.
c. You are given a model flagpole that is 8 inches tall; is this the correct size? If not, how tall does it need to be?
d. You have a model flag that is 5 by 6.3 inches. Are the model flag and original flag similar figures? If not, what would the model flag dimensions need to be? What is the scale factor?
e. Refer to the model in part c. What is the ratio of the perimeter of the model flag in comparison to the original flag?
f. Refer to the model in part d. What is the ratio of the area of the model flag in comparison to the original flag?
g. What is the relationship between the ratios of perimeter and area?
After considering all the given data we conclude that the generated answers to the sub questions are
a) 120 feet
b) 1200 inches
c) 120 inches tall
d) 72
e) 1
f) 1
g) proportional
a. To evaluate the height of the flagpole needed to support a 30 by 42 feet flag, we can apply the ratio of the height of a flagpole to the width of any flag which is 4 to 1.
This projects that the height of the flagpole is be four times the width of the flag. The width of the flag is 30 feet, so the height of the flagpole should be 4 × 30 feet = 120 feet.
b. If the individual have a model of Ft. McHenry that you need to add a flagpole to that will be proportional to the real pole at the fort and the ratio of the model is 1 inch to 10 feet, then you can apply this ratio to determine how tall the individuals model flagpole should be.
The real pole at Fort McHenry is 120 feet tall (as determined in part a), so you can multiply this by 10
10 × 120 = 1200
to get 1200 inches. This means that your model flagpole should be 1200 inches tall.
c. It is given that a model flagpole that is 8 inches tall; this is not the correct size. To evaluate how tall it needs to be, we can use the same ratio as in part b.
The real pole at Fort McHenry is 120 feet tall (as determined in part a), so you can multiply this by 10 to get 1200 inches.
This means that your model flagpole should be 1200/10 = 120 inches tall.
d. To evaluate if the model flag and original flag are similar figures, we can compare their corresponding sides.
The original flag has dimensions of 30 by 42 feet, which is equivalent to 360 by 504 inches. The model flag has dimensions of 5 by 6.3 inches. To determine if they are similar figures, we can compare their corresponding sides using ratios.
The ratio of the length of corresponding sides must be equal for two figures to be similar. The length of corresponding sides for these two flags are:
- Original Flag: Length = 360 inches; Width = 504 inches
- Model Flag: Length = 5 inches; Width = 6.3 inches
To compare these lengths, we can divide each length by its corresponding length on the other figure:
- Length Ratio: (360 / 5) = 72
- Width Ratio: (504 / 6.3) = 80
Since these ratios are not equal, these two flags are not similar figures.
To find out what dimensions would make them similar figures, we can use these ratios as scale factors:
Length Scale Factor: (360 / x) = 72
- Width Scale Factor: (504 / y) = 80
Evaluating for x and y gives us:
- x = (360 / 72) = 5
- y = (504 / 80) = 6.3
This means that if we scaled down the original flag by a factor of 72, its dimensions would be equivalent to those of the model flag.
e. To evaluate the ratio of the perimeter of the model flag in comparison to the original flag using the scale factor from part d:
Perimeter Scale Factor: (72 + 80) / 2 = 76
Model Flag Perimeter: (2 * (5 + 6.3)) = 23.6
- Original Flag Perimeter: (2 * (360 + 504)) = 1688
The ratio of these perimeters is:
Perimeter Ratio: (23.6 / (1688 /76)) ≈ 1
This means that the perimeter of the model flag is approximately equal to that of the original flag.
f. To evaluate the ratio of area between these two flags using scale factor from part d:
- Area Scale Factor: (72 × 80) = 5760
- Model Flag Area: (5 × 6.3) ≈ 31.5
- Original Flag Area: (360 × 504) ≈ 181440
The ratio of these areas is:
Area Ratio: (31.5 / (181440 /5760)) ≈ 1
This means that area of model flag is approximately equal to that of original flag.
g. Here relationship between ratios of perimeter and area is that they are both proportional to each other.
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For a swimming pool what is the difference between the following units of measure cubic feet in gallons
