Answer:
x^3 + x^2 - 5x + 3
Given u=12i-3j and v=-5i+11j, what is u x v?
Answer:
117
Step-by-step explanation:
You want the cross product of vectors u = (12i -3j) and v = (-5i +11j).
Cross productThe cross product of 2-dimensional vectors is a scalar that is effectively the determinant of the matrix of coefficients.
u×v = (12)(11) -(-3)(-5) = 132 -15
u×v = 117
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Based on the scenario, determine if it would be better to use the mean or median to describe the data set.
1 Workers at a plant are trying to show that they work too many hours. There are five part-time workers along with ten full time workersWhat summary statistic would best defend their position?
2Mrs. Smith is trying to show that her class did really well on the last test. She has four students that should have been in honors mathbut instead stayed in regular math. What summary statistic should she use to defend her position?
3. A CEO is trying to determine the average salary of his workersHe has some workers that work part- time and some very highly paid workersIf he wants a true idea of the average salarywhat summary statistic should he use?
4. Henry is trying to determine his average test grade in a class. All of his grades have been within five points of each other. He needs the average in order to calculate his overall gradeWhat summary statistic should he use?
____median
____median
____mean
____mean
1. It would be better to use the median to describe the data set.
2. It would be better to use the median to describe the data set.
3. It would be better to use the mean to describe the data set as the average salary of the workers is to be calculated.
4. It would be better to use the mean to describe the data set as the average test grade of the class is to be calculated.
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In a study conducted by the Department of Mechanical Engineering at Virginia Tech, the steel rods supplied by two different companies were compared. Ten sample springs were made out of the steel rods supplied by each company, and a measure of flexibility was recorded for each. The data are as follows:
Company A: 9.3; 8.8; 6.8; 8.7; 8.5; 6.7; 8.0; 6.5; 9.2; 7.0
Company B: 11.0; 9.8; 9.9; 10.2; 10.1; 9.7; 11.0; 11.1; 10.2; 9.6
i. Calculate the sample mean and median for the data for the two companies.
ii. Plot the data for the two companies on the same line/chart and give your impression regarding any apparent differences between the two.
iii. Is there any relation between the two companies? Compare using the 90% confidence interval of the mean.
iv. Which company you will recommend
i. The sample mean and median for the data for the two companies are 8.1 and 8.25 respectively.
ii. The line graph of the data is illustrated below.
iii. Yes, The steel rods supplied by Company B may be more flexible than those supplied by Company A.
iv. If you are looking for steel rods with higher flexibility, I would recommend Company B based on the higher median, the apparent differences in the box and whisker plot, and the confidence interval indicating a higher mean flexibility for their rods.
For Company A, the sample mean can be calculated by adding all the values and dividing by the number of values:
Mean of Company A = (9.3 + 8.8 + 6.8 + 8.7 + 8.5 + 6.7 + 8.0 + 6.5 + 9.2 + 7.0) / 10 = 8.1
To find the median, we first need to arrange the data in ascending order:
6.5, 6.7, 6.8, 7.0, 8.0, 8.5, 8.7, 8.8, 9.2, 9.3
Since there are an even number of values, the median is the average of the two middle values:
Median of Company A = (8.0 + 8.5) / 2 = 8.25
For Company B, the sample mean can be calculated similarly:
Mean of Company B = (11.0 + 9.8 + 9.9 + 10.2 + 10.1 + 9.7 + 11.0 + 11.1 + 10.2 + 9.6) / 10 = 10.2
Arranging the data in ascending order, we get:
9.6, 9.7, 9.8, 9.9, 10.1, 10.2, 10.2, 10.2, 11.0, 11.1
Since there are an odd number of values, the median is the middle value:
Median of Company B = 10.2
Next, let's plot the data for both companies on the same chart and observe any apparent differences. We can use a box and whisker plot to do this.
Looking at the box and whisker plot, we can see that the median of Company B (represented by the line in the middle of the box) is higher than the median of Company A. Additionally, the box for Company B is taller than the box for Company A, indicating that the range of values for Company B is greater than that of Company A. These observations suggest that the steel rods supplied by Company B may be more flexible than those supplied by Company A.
To determine if there is a significant difference between the means of the two companies, we can use a 90% confidence interval of the mean. This interval gives us a range within which we can be 90% confident that the true population mean lies.
Using a t-distribution with 18 degrees of freedom (10 + 10 - 2), we can find the 90% confidence interval for the difference between the means of the two companies. The formula for the confidence interval is:
Difference in means ± (t-value x standard error of difference in means)
The t-value for a 90% confidence interval with 18 degrees of freedom is approximately 1.734.
Now, we can calculate the margin of error by multiplying the t-value (1.734) by the standard error:
Margin of Error = 1.734 * 0.393 ≈ 0.682
Finally, we can construct the 90% confidence interval for the difference in means as:
Difference in means ± Margin of Error
Calculating the difference in means (mean of Company B - mean of Company A), we have:
Difference in means = 10.2 - 8.1 = 2.1
Therefore, the 90% confidence interval is:
2.1 ± 0.682
This means that we can be 90% confident that the true population mean difference between the two companies' steel rods lies between 1.418 and 2.782.
Based on this analysis, we can conclude that Company B tends to supply steel rods that are more flexible compared to Company A. However, it's important to note that this study was conducted on a small sample size, so further investigation with larger sample sizes would be beneficial to confirm the findings.
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A graph has quantity on the x-axis and price on the y-axis. A supply line goes through (10, 25), (20, 30), (30, 35), (40, 40).A graph has quantity on the x-axis and price on the y-axis. A demand line goes through (10, 40), (20, 30), (30, 20), (40, 10). Based on the supply graph and the demand graph shown above, what is the price at the point of equilibrium? a. 20 b. 30 c. 40 d. There is not enough information given to determine the point of equilibrium. A graph has quantity on the x-axis and price on the y-axis. A supply line goes through (10, 25), (20, 30), (30, 35), (40, 40).A graph has quantity on the x-axis and price on the y-axis. A demand line goes through (10, 40), (20, 30), (30, 20), (40, 10). Based on the supply graph and the demand graph shown above, what is the price at the point of equilibrium? a. 20 b. 30 c. 40 d. There is not enough information given to determine the point of equilibrium. A graph has quantity on the x-axis and price on the y-axis. A supply line goes through (10, 25), (20, 30), (30, 35), (40, 40).A graph has quantity on the x-axis and price on the y-axis. A demand line goes through (10, 40), (20, 30), (30, 20), (40, 10). Based on the supply graph and the demand graph shown above, what is the price at the point of equilibrium? a. 20 b. 30 c. 40 d. There is not enough information given to determine the point of equilibrium.
Y=-10x+1 with x being -5
Answer:
Y=-10x+1 with x being -5
y = -10 *-5 +1
y = -50+1
y =-49
The current of a river is 2 miles per hour. A boat travels to a point 15 miles upstream and back in 4
hours. What is the speed of the boat in still water?
Using the relationship of distance, time and speed, the speed of the boat in still water is 8mi/hr
What is the speed of the boat in still water?To determine the speed of the boat in still water, we can write an equation to represent this.
The speed as it travels upstream = x - 2
The speed as it travels downstream = x + 2
The total distance travelled by the boat = 15 + 15 = 30mi
Let's write an equation to represent this;
15/(x - 2) + 15/(x + 2) = 4
simplifying this;
15(x + 2) + 15(x - 2) = 4(x - 2)(x + 2)
15x + 30 + 15x - 30 = 4x² - 16
30x = 4x² - 16
4x² - 30x - 16 = 0
Solving for x;
x = -0.5, 8
But since the speed can't be negative, the speed is 8 mi/hr
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During an experiment, 2 mL of solution evaporates from a beaker each minute. After 5 minutes, there are 50.25 ml of the solution remaining. Write an equation in slope-intercept form that represents the amount of solution y in the beaker x minutes after the start of the experiment.
An equation in slope-intercept form that represents the amount of solution y in the beaker x minutes after the start of the experiment is y = 9.65x + 2.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would find the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (50.25 - 2)/(5 - 0)
Slope (m) = 48.25/5
Slope (m) = 9.65.
At data point (0, 2) and a slope of 9.65, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 2 = 9.65(x - 0)
y = 9.65x + 2
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Of all the registered automobiles in Colorado, 5% fail the state emissions test. Ten automobiles are selected at random to undergo an emissions test. Round the answers to at least four decimal places.
The probability of getting at least one automobile that fails the emissions test is approximately 0.4013 or 40.13%.
what is binomial distribution?The number of successes in a certain number of independent trials is modelled by the binomial distribution, which has just two potential outcomes for each trial, commonly referred to as "success" and "failure."
We can solve this problem by using the binomial distribution formula:
[tex]P(X=k) = (n\ choose\ k) * p^k * (1-p)^{(n-k)[/tex]
where:
P(X=k) is the probability of getting exactly k automobiles that fail the emissions test
n is the number of automobiles being tested, in this case, n = 10
k is the number of automobiles that fail the emissions test
p is the probability of a single automobile failing the emissions test, in this case, p = 0.05
Using this formula, we can calculate the probability of getting exactly k failures for k = 0, 1, 2, ..., 10, and then add up these probabilities to get the probability of getting at least one failure.
The probability of getting exactly k failures is:
[tex]P(X=k) = (10\ choose\ k) * 0.05^k * 0.95^{(10-k)[/tex]
Using a calculator or statistical software, we can calculate these probabilities:
[tex]P(X=0) = (10 choose 0) * 0.05^0 * 0.95^10 = 0.5987\\P(X=1) = (10 choose 1) * 0.05^1 * 0.95^9 = 0.3151\\P(X=2) = (10 choose 2) * 0.05^2 * 0.95^8 = 0.0746\\P(X=3) = (10 choose 3) * 0.05^3 * 0.95^7 = 0.0119\\P(X=4) = (10 choose 4) * 0.05^4 * 0.95^6 = 0.0013\\P(X=5) = (10 choose 5) * 0.05^5 * 0.95^5 = 0.0001\\[/tex]
[tex]P(X=6) = (10 choose 6) * 0.05^6 * 0.95^4 = 0.0000\\P(X=7) = (10 choose 7) * 0.05^7 * 0.95^3 = 0.0000\\P(X=8) = (10 choose 8) * 0.05^8 * 0.95^2 = 0.0000\\P(X=9) = (10 choose 9) * 0.05^9 * 0.95^1 = 0.0000\\P(X=10) = (10 choose 10) * 0.05^10 * 0.95^0 = 0.0000\\[/tex]
The probability of getting at least one failure is:
[tex]P(X > =1) = 1 - P(X=0) = 1 - 0.5987 = 0.4013[/tex]
Therefore, the probability of getting at least one automobile that fails the emissions test is approximately 0.4013 or 40.13%.
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Write a slope-intercept equation for a line passing(3,-2) through the point that is parallel to the line 3X+4Y= 9. Then write a second equation for a line passing through the point (3,-2) that is perpendicular to the line 3X+4Y= 9.
3.4 MIXED FACTORING
1. Utilize all of the strategies for factoring in order to factor the following polynomials.
Reminder: Combine like-terms prior to factoring.
2xy + 30x^2 - xy - 16y^4 - yx - 5x^2
The factor of 2xy + 30x^2 - xy - 16y^4 - yx - 5x^2 is 25x2−16y4=(5x+4y2)(5x−4y2)
We are given that;
2xy + 30x^2 - xy - 16y^4 - yx - 5x^2
Now,
Combine like terms by adding or subtracting the coefficients of the same variables. For example, 2xy - xy - yx = 0xy, and 30x^2 - 5x^2 = 25x^2. The polynomial becomes:
25x2−16y4
Check if there is a common factor for all the terms. In this case, there is no common factor other than 1, so we cannot use the greatest common factor method.
Check if the polynomial is a difference of two squares, which means it has the form a2−b2. In this case, we can see that both terms are perfect squares: 25x2=(5x)2 and 16y4=(4y2)2. Therefore, we can use the difference of two squares formula:
a2−b2=(a+b)(a−b)
Substituting a=5x and b=4y2, we get:
25x2−16y4=(5x+4y2)(5x−4y2)
Check if each factor can be further factored using any of the methods. In this case, neither factor can be further factored, so we are done.
Therefore, by factorization the answer will be 25x2−16y4=(5x+4y2)(5x−4y2)
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if you divide 781.253 by 100, what will be the place value of 2
Answer:
When you divide 781.253 by 100, you get 7.81253 as the result.
The digit 2 is in the hundredths place in the dividend 781.253. Since we are dividing by 100, which has two decimal places, we move the decimal point two places to the left in the dividend to get the quotient.
Therefore, the digit 2 is in the ten-thousandths place in the quotient 7.81253.
The mean daily demand for water, in millions of gallons, in a local city is 300, with a standard deviation of 30. Every morning the water treatment plant produces 380 million gallons of water. What is the probability that the water will run out on a given day, if the mean daily demand of water is normally distributed?
The probability that the water will run out on a given day is 0.0038.
What is the probability that water will run out?To find the probability that the demand for water on a given day exceeds the supply of 380 million gallons, we use the standard normal distribution to standardize the value of 380 million gallons as follows:
z = (x - µ) / σwhere;
x = of 380 million gallons,
µ is the mean daily demand of water = 300 million gallons,
σ is the standard deviation = 30 million gallons.
Substituting the given values:
z = (380 - 300) / 30
z = 2.67
Using a calculator, the probability that a standard normal random variable is greater than 2.67 is 0.0038.
Therefore, the probability that the water will run out on a given day is 0.0038.
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Car A travels 221.5 km at a given time, while car B travels 1.2 times the distance car A travels at the same time. What is the distance car B travels during that time?
Answer:
Distance that car B travels =1.2× distance that car A travels
=1.2×221.5=265.8 km
Answer:
car B travels a distance of 265.8 km during the same time.
Step-by-step explanation:
Car A travels 221.5 km at a given time.
To find the distance traveled by car B, which is 1.2 times the distance traveled by car A, we can multiply the distance of car A by 1.2:
Distance of Car B = 1.2 * Distance of Car A
Distance of Car B = 1.2 * 221.5 km
Distance of Car B = 265.8 km
Therefore, car B travels a distance of 265.8 km during the same time.
Mariana is making a large pot of pasta. She mixes together 518 pounds of pasta, 6 pounds of sauce, and 478
pounds of onions.
To find out how many 12
pound servings can she make, which two equations would you need?
A.
518+478+6=16
B.
518+478−6=4
C.
4÷12=8
D.
16÷12=32
E.
16×12=8
We need to use equations C and D:
C. 4 ÷ 12 = 1/3
D. 16 ÷ 12 = 4/3
To find out how many 12-pound servings Mariana can makeWe need to divide the total amount of pasta by 12. Therefore, we need to use equations C and D:
C. 4 ÷ 12 = 1/3
D. 16 ÷ 12 = 4/3
Equation C shows that each serving is 1/3 of a pound
Equation D shows that Mariana can make 4/3 servings
Therefore, Mariana can make 4/3, or approximately 1.33, servings of 12 pounds each.
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Given u = - i + j v = 8i - 2j and w = - 4j find pro*j_{u}(v + w)
The projection of (v + w) onto u is (-8 √(2)i + 6 √(2)j).
Now, let's consider the given vectors u = - i + j, v = 8i - 2j, and w = - 4j. The question asks us to find the projection of vector v + w onto the vector u, denoted as proj_u(v + w). To find this projection, we need to use the dot product between the two vectors.
First, we need to calculate v + w, which is (8i - 2j) + (-4j) = 8i - 6j. Next, we calculate the dot product of u and (v + w):
u · (v + w) = (-i + j) · (8i - 6j)
= -8i + 6j - 8i + 6j
= -16i + 12j
The dot product measures the similarity between two vectors, and in this case, it gives us the component of (v + w) that is parallel to u. To find the projection of (v + w) onto u, we need to divide this component by the magnitude of u:
proj_u(v + w) = (u · (v + w)) / ||u||
= (-16i + 12j) / √(2)
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Which of the following is an exponential equation?
A.
3x + 2 = 23
B.
5 ‒ x2 = 4
C.
3x + 2 = 23
D.
7 ‒ 0.5x = 2x
Answer:
a. 3x = 23-2
3x = 21
x = 21÷3
x = 7
b. 5x - 2 = 4
5x = 4+2
5x = 6
x = 6÷5
x = 1.2
c. 3x = 23-2
3x = 21
x = 21÷3
x = 7
d. 7 = 2x+0.5x
7 = 2.5
x = 2.5÷7
x = 2.8
Tamika is seeking a loan with a simple
The interest that Tamika will be charged in interest after 24 months of borrowing $5,000 at 8% simple interest per year is $800.
What is simple interest?Simple interest is the interest system that computes interest only on the principal for each period.
Unlike the compound interest system, simple interest does not charge interest on accumulated interest and the principal.
The principal loan amount borrowed by Tamika = $5,000
The interest rate per year = 8%
The loan period = 24 months = 2 years (24/12)
Simple Interest = Principal x Rate x Period
= $800 ($5,000 x 8% x 2)
Thus, for borrowing $5,000 for 24 months of 2 years, Tamika would pay a simple interest of $800.
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Complete Question:Tamika is seeking a loan with a simple interest rate of 8% per year. If she wants to borrow $5,000, then how much will she be charged in interest after 24 months?
For the right triangle shown below, find the exact values of:
sinB b)tanA c)cosA
Answer:
17
Step-by-step explanation:
11+6=17
(a) The exact value of sin B is 6 / 12.53
(b) The exact value of tan A is 11 / 6
(c) The exact value of cos A is 6 / 11
What is the value of sin (B) , tan (A) and cos (A)?The value of sin (B), cos (A) and tan (A) is calculated by applying trigonometry ratio as follows;
The trigonometry ratio is simplified as;
SOH CAH TOA;
SOH ----> sin θ = opposite side / hypothenuse side
CAH -----> cos θ = adjacent side / hypothenuse side
TOA ------> tan θ = opposite side / adjacent side
The value of the hypotenuse side of the right triangle is;
L = √ (6² + 11²)
L = 12.53
(a) The exact value of sin B is;
sin B = 6 / 12.53
(b) The exact value of tan A is;
tan A = 11 / 6
(c) The exact value of cos A is;
cos A = 6 / 11
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Solids A and B are similar. Use the given information and scale factor k from solid A to solid B to find the surface area of solid B.
Prism A has a surface area of 805 square feet and the and k=1/5
Answer:
32.2 ft²---------------------
We know that area is the product of two dimensions.
Hence we consider the square of the scale factor when comparing areas of similar figures.
The surface area of solid B is k² times the surface area of solid A:
S(B) = k²S(A)Substitute and calculate:
S(B) = (1/5)²(805) = 805/25 = 32.2 ft²7
35cm
42cm
X =
6cm
cm
N
HELP ME FAST GUYS!! Asap
The value of x in the polygon is 5 centimetres.
How to find the side of similar polygon?A polygon is a two-dimensional geometric figure that has a particular number of sides.
Two polygons are similar if their corresponding angles are congruent and the corresponding sides have a constant ratio .
Therefore, using the ratio of the similar polygon, let's find the value of x as follows:
35 / x = 42 / 6
cross multiply
35 × 6 = 42x
210 = 42x
divide both sides of the equation by 42
x = 210 / 42
x = 5 cm
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Can anyone help me answer this question?
f(x) = 5x^3 + 3x^2 - x/ x+2 and g(x) = x^2 - 1/ x - 1. Find the limit of f^2(x) as x approaches 2
The function limit of f(x) as x approaches 2 is 67 and the limit of f²(x) as x approaches 2 is 4489.
The function f(x) can be rewritten as:
f(x) = (5x³ + 3x² - x)/(x+2)
Using direct substitution, we see that f(2) is undefined, as the denominator of the function becomes 0.
To evaluate the limit, we can use L'Hopital's rule:
[tex]\lim_{x \to 2\[/tex] f(x) = lim x→2 (5x³ + 3x² - x)/(x+2)
= [tex]\lim_{x \to 2\[/tex] (15x² + 6x - 1)/(1)
= (15(2)² + 6(2) - 1)/(1)
= 67
To find the limit of f²(x) as x approaches 2, we can simply square the limit:
f(x) = [tex]\lim_{x \to 2\}[/tex]f²(x)
= [tex]\lim_{x \to 2[/tex] f²(x)
= 67²
= 4489
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PLS HELP
The number of hours a student spent studying each week for 9 weeks is shown.
9, 4.5, 8, 6, 9.5, 5, 6.5, 14, 4
What is the value of the range for this set of data?
The table below represents a linear equation
Which function has a greater slope and greater y-intercept than the linear function represented in the table?
A. y = 2x + 8.5
B. y = 3x +7.5
C. y = 5x + 6.5
D. y = 10x + 5.5
The function that has a greater slope and greater y-intercept than the linear function represented in the table is,
⇒ y = 3x + 7.5
We have to given that;
The table below represents a linear equation.
Now, The equation of line is,
Take two points (- 1, 5) and (1, 9)
⇒ y - 5 = (9 - 5) / (1 + 1) (x + 1)
⇒ y - 5 = 4/2 (x + 1)
⇒ y - 5 = 2 (x+ 1)
⇒ y - 5 = 2x + 2
⇒ y = 2x + 7
Hence, By options,
The function that has a greater slope and greater y-intercept than the linear function represented in the table is,
⇒ y = 3x + 7.5
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What is the area of this figure? 11 mm 3 mm 2 mm 2 mm 4 mm 2 mm 5 mm 3 mm Write your answer using decimals. Use 3.14 for л.
Answer: 116.985 mm2
Step-by-step explanation:
a 7 cm times 5 cm rectangle sits inside a circle with a radius of 6 cm
The shaded area of the portion as shown in the diagram is 78.04 cm².
What is area?Area is the region bounded by a plane shape.
To calculate the shaded area of the portion, we use the formula below
Formula:
A = πr²-lw.................. Equation 1Where:
A = Area of the shaded portionr = Radius of the circlel = Length of the rectanglew = Width of the rectangleFrom the question,
Given:
r = 6 cml = 7 cmw = 5 cmSubstitute these values into equation 1
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Complete question: A 7 cm times 5 cm rectangle sits inside a circle with a radius of 6 cm. Calculate the area of the shaded portion.
36 is 15% of what number
The slope of the line whose equation is 5x - 3y = 4 is 4/5 5/3 -3/5
The slope of the relation with the equation 5x - 3y = 4 is 5/3
Calculating the slope of the relationTo find the slope of the line whose equation is 5x - 3y = 4, we need to rearrange the equation to be in slope-intercept form, y = mx + b, where m is the slope of the line.
First, we'll subtract 5x from both sides:
-3y = -5x + 4
Next, we'll divide both sides by -3 to isolate y:
y = (5/3)x - 4/3
Now we can see that the slope of the line is 5/3.
So the correct answer is: 5/3
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Why does income for a family tend to go up when two single persons marry?
A. Newly married couples tend to have two earners.
B. Married people work longer hours than single people.
C. Two people can live as cheaply as one.
D. The Federal government's marriage tax favors married people.
Answer:
A.) Newly married couples tend to have two earners.
Step-by-step explanation:
When newly married couples first start off marriage, they tend to both work to make stable income since they recently had to work to make money for only their selves, which is why they both tend to have two earners.
PLEASE HELP!!!
The surface area of a triangular pyramid is 400 square meters. The surface area of a similar triangular pyramid is 25 square meters.
What is the ratio of corresponding dimensions of the smaller pyramid to the larger pyramid?
Enter your answer by filling in the boxes.
Answer:
can i get a picture\
Step-by-step explanation:
thanks
Answer:
Step-by-step explanation:
1:4
Solve for 10 and 12 please and thank you
Answer:
10. 120 Degrees 12. 60 Degrees
Step-by-step explanation:
#12. Since CAD is 30, and BAD is a 90 degree angle, angle BAF is 60 degrees. Since BAF is 60 degrees and FAE and BAF are vertical angles, they have the same angle measure. 60 Degrees.
#10. Since BAF is 60, and FAE and BAF are on a line, we can do 180-60 to get the measure in degrees of that angle. FAE = 120 Degrees.
Answer:
Step-by-step explanation:
10. somewhere between 126 and 129, i feel its 128
12. between 60 and 65