Answer:
Step-by-step explanation:
x = 2
step-by-step explanation:
if sr parallel to ba then the sides bc and ac are in proportion, that is
\frac{sb}{cs} = \frac{ra}{cr} ← substitute values
\frac{4x+1}{2x} = \frac{13.5}{6} ( cross- multiply )
27x = 6(4x + 1)
27x = 24x + 6 ( subtract 24x from both sides )
3x = 6 ( divide both sides by 3 )
x = 2
Neils refrigerator has stopped working and he needs to get a new one. He purchases a new ref for P36,700. He paid a 10% deposit and obtain a loan for the balance. The interest charged on the loan was 7.5% APR compounded annually. He repaid the loan and interest in equal monthly installment for over a period of two years. Calculate the loan he made and the total amount to be repaid.
a) The loan that Neil made for the purchase of a new refrigerator is P33,030.
b) The total amount to be repaid over a period of two years is P35,672.16.
What is the loan amount?The loan amount is the difference between the purchase price of a new refrigerator and the deposit (down payment).
The total amount to be repaid over the loan period includes the loan amount and the interest.
These amounts can be computed using an online finance calculator, including the monthly payments.
The cost of a new refrigerator = P36,700
Deposit (down payment) = 10%
The amount of the loan = P33,030 (P36,700 - P3,670)
N (# of periods) = 24 months (2 years x 12)
I/Y (Interest per year) = 7.5%
PV (Present Value) = P33,030
FV (Future Value) = P0
Results:
PMT = P1,486.34
Sum of all periodic payments = P35,672.16 ($1,486.34 x 24)
Total Interest = P2,642.16
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Dr. Sparrow is a social psychologist who studies romantic relationships. Several researchers have found that there is a link between income and marital satisfaction (e.g., Dakin & Wampler, 2008). Dr. Sparrow is curious as to whether there is a causal link between the two variables, such that having a higher income causes higher levels of marital satisfaction. He is confident that he cannot reasonably or ethically manipulate people's income level, so he decides to use a multivariate design. He is also curious as to whether there is a causal link between these two variables or if two other variables (number of arguments and life satisfaction) can explain the relationship. He measures his three variables in a sample of 124 married couples recruited from a local community center. Below are his results.
DV: Marital Satisfaction
Variable Beta (b) Significance ( p)
Income
.69
.03
Number of arguments
-.73
.01
Life satisfaction
.13
.81
Refer to Research Study 9.2 to answer the following four questions.
Given Dr. Sparrow's design, which of the following problems is his study best able to overcome?
Given Dr. Sparrow's design, his study is best able to overcome the issue of causality, as well as the issue of some potential third variables.
By using a multivariate design, Dr. Sparrow is able to examine the relationships between multiple variables simultaneously, which can help to identify the potential influence of each variable on the outcome of interest (marital satisfaction in this case). This can help to establish a causal link between the variables if one is present, as it allows for the examination of multiple variables at the same time, rather than just two variables as in a simple bivariate design.
Additionally, by controlling for other potential confounding variables, Dr. Sparrow is able to account for the potential influence of these variables on the relationship between income and marital satisfaction, which helps to establish a more robust understanding of the potential causal link between these two variables.
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write an equation in slope intercept form that is perpendicular to y = 8 and passes through the point (-1,-8)
Answer:
Step-by-step explanation it will be 23 cups
Use the scale to help you solve the equation and find the value of x. Enter the
value of x below.
x+ 6 = 12
X =
Answer:
x=6
Step-by-step explanation:
12-6=6 or 6+6=12
In art class students are mixing blue and red paint to make purple paint. Hassan
mixes 1 cup of blue paint and 3 cups of red paint. Skylar mixes 5 cups of blue paint
and 3 cups of red paint. Whose purple paint will be bluer?
The person whose purple paint will be bluer is Skylar.
Whose purple paint will be bluer?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this case, Hassan mixes 1 cup of blue paint and 3 cups of red paint. The percentage for blue paint will be:
= 1 / (1 + 3) × 100
= 1/4 × 100
= 25%
Skylar mixes 5 cups of blue paint and 3 cups of red paint. The percentage for blue will be:
= 5 / (5 + 3) × 100
= 5/8 × 100
= 62.5%
Skylar has bluer paint.
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Describe the graph of proportional relationship represented by the equation Y equals eight minus 5X
The description of the proportional relationship represented by the equation y = 8 - 5x is A. The graph is a line that goes through points (0, 8) and ( 4, -12 ).
How to describe the graph ?The graph is given in the form of a linear equation which is y = mx + b. In this equation, b is the y - intercept, or the point the line crosses the y - axis when x is 0. This point on y = 8 - 5x, is 8.
If the line passes through the x axis at point 4, then the y - intercept would be :
= 8 - 5 ( 4)
= 8 - 20
= - 12
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Options for this question are:
The graph is a line that goes through points (0, 8) and ( 4, -12 ).The graph is a line that goes through points (0, 5) and (15, 2).The graph is a line that goes through points (0, 4) and (12 , 1).The graph is a line that goes through points (0, 5) and (1, 12 ).The graph of a function f is illustrated below. What is the graph of the inverse function of f?
The graph of the inverse function of f(x) is given by the image shown at the end of the answer.
How to obtain the inverse function?The function in this problem is defined as follows:
f(x) = 1/x + 4.
The definition of the function is given because of the asymptotes as follows:
Vertical asymptote at x = 0 -> function is not defined at x = 0.Horizontal asymptote at y = 4 -> when x goes to infinity, y goes to 4.To obtain the inverse of a function y = f(x), first the variables y and x are exchanged, as follows:
x = 1/y + 4.
Then the variable y has to be isolated, as follows:
1/y = (x - 4).
y(x - 4) = 1
y = 1/(x - 4)
Meaning that the inverse function is defined as follows:
[tex]f^{-1}(x) = \frac{1}{x - 4}[/tex]
Which has the graph given by the image shown at the end of the answer.
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Answer: B
Step-by-step explanation: literally just did it
If you invest $4064 in an account that pays simple interest of 7% How much interest will you have earned after 6 years?
Answer:
You would have $6055.36 in 7 years.
Step-by-step explanation:
Using the order of operations, which operation in the
expression 3×2-2³ ÷ 4 should be completed first?
A) Multiply 3 and 2.
B) Divide 2^3 by 4
C) Cube 2.
D)
Subtract 2^3 from 2.
Answer:
C) Cube 2.
Step-by-step explanation:
Cubing 2 means to take 3 as an exponent of 2.
Parantheses
Exponents ==> 2³
Multiplication ==> 3*2
Division ==> 2³ ÷ 4
Addition
Subtraction ==> 2-2³
In PEMDAS, Exponents is the second highest priority in an equation, so it comes first in 3×2-2³ ÷ 4 as there is no parantheses.
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f ( x ) = ( x − 2 ) ( x + 4 ) ( x + 5 ) ( x − 1 ) ( x − 9 ) has zeros at x = -5, x = -4, x = 1, x = 2, x = 9
What is the sign of F on the interval -4 < x < 1?
The sign of F on the interval -4<x<1 is 0
How to do substitution in a function?We know that in mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y.
The given function is
f(x)=(x-2)(x+4)(x+5)(x-1)(x-9)
The Interval is given as -4<x<1
Substituting the values of x in the function we have
f(x)=(-5-2)(-4+4)(1+5)(2-1)(9-9)
This implies that
f(x)=(0)(0)(6)(1)(0)
Multiplying the brackets to have
f(x)=0
In conclusion, the sign of F on the interval -4<x<1 is 0
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Convert 32/5 to a mixed number. Step-by-step explanation.
Answer:
Step-by-step explanation:
First think about how many times 5 goes into 32. That would be 6 times since 6*5 is 30.
Now we just have the 2 from the 32 left over. The two will be put on top of the 5 from 32/5 so it will be 2/5
Put the two together and it would be 6 and 2/5
how can you divide polynomials
Polynomials can be divided using long division method and
synthetic division method.
What is a polynomial?
Algebraic expressions which are made up of coefficients and variables are called polynomials.
For example x + 3, 3y² -10, r³, t³ + 4t³ - 80, etc.
Polynomials can be classified as monomials, binomials and trinomials based upon the number of terms present.
According to the given question:
There are two methods that can be employed while dividing two given polynomials:
1. Long Division Method
The long division method is the most frequent and general method for dividing polynomials by binomials or any other form of polynomials.
Steps:
Step 1: Divide the dividend’s first term by the divisor’s first term, and use it as the quotient’s first term.
Step 2: Multiply the divisor, then place the product beneath the dividend
Step 3: To make a new polynomial, subtract.
Step 4: Use the new polynomial obtained after subtraction to repeat the operation.
2. Synthetic Division Method
It is a technique for dividing a polynomial by a linear binomial using only the coefficient values. We write the polynomials in standard form from the greatest degree term to the lowest degree term in this manner.
Steps:
Step 1: Ensure that the divisor is in the form of x − k.
Step 2: Write the dividend coefficients on the right and k on the left to set up the division.
Step 3: Now, reduce the coefficient of the dividend’s highest degree term to zero.
Step 4: Multiply k by that leading coefficient and write the product below the second coefficient on the dividend’s left side.
Step 5: Multiply the numbers in the second column.
Step 6: Multiply k by the number obtained in step 5 and write the result in the next column to the right.
Step 7: Finally, we’ll write the final solution, which will be one degree below the dividend.
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a quadrilateral has vertices (2,0), (0,-2), (-2,4) and (-4,2) which special quadrilateral is formed by connecting the midpoints of the sides a. kite
b. rectangle
c. trapezoid
b. rhombus
The quadrilateral that has vertices (2,0), (0,-2), (-2,4) and (-4,2) is option
b. rectangle
Why is it a rectangle?To determine the special quadrilateral that is formed by connecting the midpoints of the sides of the quadrilateral with vertices (2,0), (0,-2), (-2,4) and (-4,2), we can find the midpoints of each side and then determine the shape formed by these points.
The midpoint of a line segment is the point that is exactly halfway between the two endpoints of the line segment. To find the midpoint of a line segment, we can take the average of the x-coordinates of the endpoints and the average of the y-coordinates of the endpoints.
We can find the midpoint of the side between (2,0) and (0,-2) by taking the average of the x-coordinates (2 and 0) and the average of the y-coordinates (0 and -2), which gives us the point (1,-1).
We can find the midpoint of the side between (0,-2) and (-2,4) by taking the average of the x-coordinates (0 and -2) and the average of the y-coordinates (-2 and 4), which gives us the point (-1,1).
We can find the midpoint of the side between (-2,4) and (-4,2) by taking the average of the x-coordinates (-2 and -4) and the average of the y-coordinates (4 and 2), which gives us the point (-3,3).
We can find the midpoint of the side between (-4,2) and (2,0) by taking the average of the x-coordinates (-4 and 2) and the average of the y-coordinates (2 and 0), which gives us the point (-1,1).
Therefore, the special quadrilateral formed by connecting the midpoints of the sides of the given quadrilateral is a rectangle.
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A barrel of U.S. oil is 42 gallons. How many liters is this? Round off to the nearest whole number. Note: 1 gallon = 4 quarts. Strategy: you must convert from gallons quarts liters. Use two conversion factors ( 1 gallon = 4 quarts )
Answer:
158 liters.
Step-by-step explanation:
G=gallons
L=Liters
Q=Quarts
42G * 4Q = 168Q
1Q = 3.785L
3.785L * 42G = 158L or another way is to go by the formula is by dividing the volume value by 1.057:
168Q divide by 1.057 = 158
Consider 4x + 12 ≤ 28. Which value of x makes the given inequality TRUE?
Responses
A 1010
B 77
C 33
D 6
We know that,
Inequality-
In mathematics, the relationship between two expressions or values that are not equal is called an inequality.
Group terms with the same variable and move the constant to the other side of the inequality
What causes inequality?
Inequality image result
The main factors behind the widening domestic income inequality mentioned in the literature include technological progress, globalization, commodity price cycles, and domestic economic policies such as redistributive fiscal policies, labor and product market policies. It is included.
According to the question,
Given data in the question,
4x + 12 ≤ 28
Substrating (28-12)=16
We can say that,
4x ≤ 16
16 divided by 4.
Therefore,
(16/4)=
x<4
the value of x is less than 4,
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3 is the value of x which makes the given inequality true.
What is Inequality?A relationship that compares two numbers or other mathematical expressions in an unequal way is known as an inequality in mathematics. On the number line, it is most frequently used to compare the sizes of two numbers. To represent various types of inequalities, a variety of notations are used:
A < B, such as a, denotes that an is greater than b.
A > B indicates that an is greater than b.
A and b are not equivalent in either scenario. As a result, an is strictly less than or strictly greater than b, and these relationships are referred to as strict inequalities. Equivalence is disregarded.
According to the question,
Given data in the question,
4x + 12 ≤ 28
Substrating (28-12)=16
We can say that,
4x ≤ 16
16 divided by 4.
Therefore,
(16/4)=
x<4
the value of x is less than 4,
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When a firm applies statistical techniques to develop and maintain its ability to produce high-quality goods and services, it is implementing statistical _____.
When a company applies statistical techniques to develop and support its ability to produce high-quality goods and services, it is implementing statistical quality control.
What is quality control?Quality control (QC) is a procedure or set of actions intended to make sure that a manufactured product or performed service complies to a described set of quality standard or meets the conditions of the client or customer. QC is similar to quality assurance (QA), but not exactly same.
The quality control applied in a business is greatly dependent on the product or the industry. For example, in food and drink manufacturing, quality control also includes certifying the product will not make a consumer unwell, so the company does chemical and microbiological examination of samples from the production line.
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A circle with center H is shown in the figure below
A researcher performs six independent hypothesis tests each at the 5% significance level. Determine the probability of observing at most two Type Errors. (Round your final answer to the nearest hundredth of a percent, e.g., 12.63% Rounding counts
At the 5% significance level, a researcher conducts six separate hypothesis tests. the likelihood of finding two or fewer Type Errors.
What is the 5 step process in statistics?Declare your null and alternate hypotheses in Step 1. Data collection is step two. Perform a statistical test in step three. In step four, you must choose whether to reject or not to reject your null hypothesis. Deliver your results in Step 5. Five steps make up the statistical process: design the study, assemble the data, Analyze the data, draw conclusions, and take action. In a planned experiment, the variables are under the researchers' control.
Utilizing sample data, hypothesis testing is a method used to determine whether a hypothesis is tenable. The test offers proof that, given the available data, the hypothesis is plausible. By measuring and reviewing a representative sample of the population under study, statistical analysts can evaluate a theory.Procedures for testing hypotheses Identifying the null hypothesis is the first step.
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What’s greater, 9 or 9.1?
Answer:
9.1
Step-by-step explanation:
9.1 would be greater because it is basically 9 + 0.1.
Write the following number in scientific notation: 0.0003005
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the
10.
If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
Try it
Using a Grid to Estimate Perimeter
Estimate the perimeter of the figure if each block on the
grid is 1 square unit.
The perimeter of the figure is about
units.
The Perimeter of of the Figure is shown below.
What is Scale factor?To adjust the size of a figure without altering its shape, a scale factor is a number or conversion factor that is utilised. It is employed to change the size of an object. If the original figure's dimensions and the dilated (increased or lowered) figure's dimensions are known, the scale factor can be determined.
Gives:
We have area of each small square is 1 sq cm.
So, We have three grids a
For figure (i) there are 11 small square
So, Perimeter of the given figure =( 18 ×1)cm
=18 cm
For figure (ii) there are 13
Perimeter of the given figure =(28×1)cm
=28 cm
For figure (iii) there are 13
Perimeter of the given figure =(28×1)cm=28 cm.
=28 cm
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In ΔVWX, x = 77 cm, ∠X=74° and ∠V=16°. Find the length of w, to the nearest 10th of a centimeter.
Answer:
The length of w is 50.0 cm.
Step-by-step explanation:
To find the length of w, we can use the Law of Sines:
w / sin V = x / sin X
Plugging in the values given in the question, we get:
w / sin 16° = 77 cm / sin 74°
Solving for w, we get:
w = 50.0 cm
Rounding to the nearest 10th of a centimeter, we get:
w = 50.0 cm
Therefore, the length of w is 50.0 cm.
Answer:
w=80.1 cm
Step-by-step explanation:
According to the Law of Sines:
[tex]\frac{\sin(\alpha)}{a}=\frac{\sin(\beta)}{b}=\frac{\sin(C)}{c}[/tex]
For this problem, let
[tex]\alpha[/tex]=∠X=74°
[tex]\beta[/tex]=∠V=16°
Since the sum of the angle measures in all triangles must equal 180°, ∠w must equal 90°. So, for this problem, let
C=∠W=90°.
And let
a=x=77 cm
c=w
So,
[tex]\frac{\sin(74)}{77\ cm}=\frac{\sin(90)}{w}\\0.01248\ cm=\frac{1}{w}\\w=80.1\ cm[/tex]
This can be checked using the Law of Sines with all values entered.
To find b, use the Pythagorean Theorem:
[tex](80.1\ cm)^2=(77\ cm)^2+b^2\\6416.01\ cm^2=5929\ cm^2+b^2\\487.01\ cm^2=b^2\\b=22.07\ cm[/tex]
So,
[tex]\frac{\sin(74)}{77\ cm}=\frac{\sin(16)}{22.07\ cm}=\frac{\sin(90)}{80.1\ cm}\\0.0125\ cm=0.0125\ cm=0.0125\ cm[/tex]
find the distance between the points (-9.3 , 6.7) and (-9.3, -5.5)
Answer:
0, -12
Step-by-step explanation:
Determine how many ounces are in 15 liters. Show every step of your work
pls help
Answer:
15 liter = 507.210848 Fluid Ounces
because 1 liter = 33.8140565 so you do 33.8140565 x 15 = 507.210848
mark me brainliest
hope this helps you
Step-by-step explanation:
the daily info newspaper charges a fee of $650 plus $80 per week to run an ad. the peoples paper charges $145 per week. for how many weeks will the total cost at the peoples paper be less expensive
The total cost at the peoples paper be less expensive will represent by the inequality 650 + 80w < 145w.
What is inequality?
In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
Given that the daily info newspaper charges a fee of $650 plus $80 per week to run an ad.
Assume that after w weeks the total cost at the peoples paper be less expensive.
To run ad. for w week, the cost will be 80w.
The total cost of material of newspaper is p(w) = 650 + 80w
The peoples paper charges $145 per week.
The peoples paper charges after w week will be f(w) = 145w.
According to the question:
p(w) < f(w)
650 + 80w < 145w
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the difference between the measure of two supplementary angles is 92. find the measure of both angles.
The measure of both angles on calculation is found to be 44° and 136° respectively.
What are supplementary angles ?
Supplementary angles are those angles that sum up to 180 degrees. For example, angle 130° and angle 50° are supplementary angles because sum of 130° and 50° is equal to 180°. Similarly, complementary angles add up to 90 degrees.
Given : difference between the measure of two supplementary angles is 92 .
Let the two angles be x and y then , x - y = 92
Since , supplementary angles add up to 180 degrees
x + y = 180 (say 1)
x - y = 92(say 2)
---------------add(1 & 2)
2x = 272
x = 272/2
x = 136 <=== this is one angle
x + y = 180
136 + y = 180
y = 180 - 136
y = 44 <=== this is the other angle
Hence , the measure of both angles on calculation is found to be 44° and 136° respectively.
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Hose A can fill 3/4s of a pool in 1 hour. Hose B can full 2/4s of the same pool in 1 hour. How long will it take to fill the pool if you use both hoses?
The time required to fill the pool by using both the hoses is 4/5 hours.
What is algebra?Algebra is the study of mathematical expressions, in which letters and other generic symbols are used to represent numbers and quantities in formulas and equations.
Given that,
Time taken by hose A to fill 3/4 of the pool = 1 hour.
And time taken by hose B to fill the 2/4 of the same pool = 1 hour.
From the given information,
Time taken by hose A to fill the whole pool = 1 x (4/3) = 4/3 hours
And time take by hose B to fill the whole pool = 1 x (4/2) = 1 x 2 = 2 hours.
The LCM of 4/3 and 2 is 4, which can be considered as total capacity of pool.
The efficiency of hose A = 4/(4/3) = 3
The efficiency of hose B = 4/2 = 2
Total time taken to fill the whole pool by using both hoses
= 4 / (3+2) = 4 / 5 hours
If both hoses are uses, then it will take 4/5 hours to fill the pool.
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The dosage of a certain medication is determined by a patient's body weight. This medication's dosage is 2.5 mg per kilogram of body weight. What would be the dose for a patient who weighs 72 pounds? (1 lb = 0.453 kg) (Doses are rounded to the nearest 25 mg.)
Show work please
Answer:
75 mg
Step-by-step explanation:
You want the dose for a 72 pound person at the rate of 2.5 mg/kg.
Unit conversionWe multiply by conversion factors that cancel unwanted units, leaving the units we want.
At the end of the unit conversion, we need to determine if the calculated dose is closer to 75 mg or 100 mg. It is less than 87.5 mg, so is closer to 75 mg.
[tex]\dfrac{2.5\text{ mg}}{\text{kg}}\times(72\text{ lb})\times\dfrac{0.453\text{ kg}}{\text{lb}}=2.5\times72\times0.453\text{ mg}\approx81.54\text{ mg}\\\\\approx\boxed{75\text{ mg}}[/tex]
__
Additional comment
We found the nearest 25 mg dose by dividing by 25 mg, and rounding the 3.26 dose result to 3 doses of 25 mg each.
Write 28 as a product of prime factors.
Answer: 2×2×7
The prime factorization of 28 = 2×2×7.
Step-by-step explanation: Do the prime factorization
28
7 4
2 2
8x10^-5
help pleaseeeeeeeeeeeeeeeeeeeeeeeee
Answer:
.00008
Step-by-step explanation:
8x10^-5 = .00008
Your moving the dot over 5 times to the left since its negative. If it was postive you wold move the dot 5 times to the right
Answer: 0.00008
Step-by-step explanation: Yes, I know there are A LOT of zeros. So, to find this answer, you would rewrite the answer like this:
- 8*10^(-5)
So, here's a little trick, you multiply 8 by 10, to get 80. Then, since it is -5, you move 5 decimal places to the LEFT. This is why there are so many zeros. I hope this explanation helped!