23
1 Which of the following numbers makes
the inequality below true?
2.5p < 14
Ap=5
Bp=6
cp=7
Dp = 8
lo What is the value of n in the countion

Answer:

x = 2.55 (rounded)

x = 2. 5454545455 (exact)

Step-by-step explanation:

We can change this sentence, into a mathematical expression and solve:

5.5 · x = 14

x = 14 / 5.5

x = 2.5454545

x = 2.55 (rounded)

Hope this helps!!

The amount of money is 4000 was invested at 3%.

Let x be the amount of money invested at 3%.

Then, the amount of money invested at 5% is 6000 - x.

The interest earned on the amount invested at 3% is 0.03x.

The interest earned on the amount invested at 5% is 0.05(6000 - x) = 300 - 0.05x.

The total interest earned is given as $220.

So, we can write the equation:

0.03x + (300 - 0.05x) = 220

Simplifying and solving for x, we get:

0.03x + 300 - 0.05x = 220

-0.02x + 300 = 220

-0.02x = -80

x = 4000

Therefore, $4000 was invested at 3%.

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Answer:

Step-by-step explanation:

1)

Congruency shortcuts:  

HL, SSS, SAS, ASA, and AAS

where S=side

A=angle

H=hypotenule

L=leg

HL is only for a right triangle

If you can prove sides and angles are congruent according to those 5 rules, you have proven the triangles are congruent

Similarity shortcuts:

AA, SAS, SSS

We have triangle similarity if (1) two pairs of angles are congruent (AA) (2) two pairs of sides are proportional and the included angles are congruent (SAS), or (3) if three pairs of sides are proportional (SSS)

2)

BG ≅ GD              >Given from image

IG ≅ GO               >Given from image

<BGI ≅ <DGO        >Vertical Angles

ΔBGI  ≅ ΔDGO        >SAS            

You have proven that the triangles are congruent because you used the shortcut by proving a side and angle and a side are congruent so SAS makes them congruent

Answer:

9576

Step-by-step explanation:

Area of the triangle × height

(1/2×28×19)×36

To find the distance between points A and B, we can use trigonometry and the given information.

Let's label the distance between A and B as "d". We know that point C is 94.4 meters away from point A. From angle A, we have the measure of 72°, and from angle C, we have the measure of 30°.

Using trigonometry, we can use the tangent function to find the value of "d".

tan(72°) = d / 94.4

To solve for "d", we can rearrange the equation:

d = tan(72°) * 94.4

Using a calculator, we can evaluate the expression:

d ≈ 4.345 * 94.4

d ≈ 408.932

Therefore, the distance between points A and B is approximately 408.932 meters.

Answer:

30015 Remainder 15

Step-by-step explanation:

Answer:

30,015  11/50

Answer:

  b.  $154,810

Step-by-step explanation:

You want to know the price of a home that can be purchased for a monthly payment of $879.32 on a 30-year loan at 5.5%.

The given table tells you the multiplier m used to find the monthly payment p from the loan amount P for different time periods and interest rates.

  p = (P/1000)×m

The table value for a 30-year loan at 5.5% is m = 5.68. Solving the equation for P, we have ...

  1000p/m = P

  1000(879.32/5.68) = P ≈ 154,809.86 ≈ 154810

You qualify for a loan of $154,810.

__

Additional comment

The multiplier 5.68 is found on row 2 (5.5%) of column 4 (30 years).

By answering the presented question, we may conclude that As a result, equation the answer is (b) $154,810.

A mathematical equation is a formula that connects two statements and denotes equivalence with the equals symbol (=). An equation is a mathematical statement that shows the equality of two mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the variables 3x + 5 and 14. A mathematical formula describes the connection between the two sentences that occur on opposite sides of a letter. The symbol and the single variable are frequently the same. As in 2x - 4 Equals 2, for instance.

To establish the purchase price of a property, we must use the monthly payment and the table supplied to determine the mortgage amount that corresponds to the monthly payment.

According to the data, the monthly payment per $1000 of mortgage for a 30-year fixed mortgage at a 5.5% interest rate is $5.68.

Hence, to calculate the mortgage amount for a $879.32 monthly payment, we may apply the following formula:

Mortgage amount = monthly payment / mortgage payment per $1000

$879.32 mortgage amount / $5.68 per $1000

Loan amount = $154,810

As a result, the purchasing price of a house is $154,810.

As a result, the answer is (b) $154,810.

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The perimeter of the rectangle is 4h + 6

An algebraic expression can be defined as an expression that is composed of terms, variables, coefficients, constants and factors.

These expressions are also made up of arithmetic operations, such as;

The formula for calculating the perimeter of a rectangle is expressed as;

Perimeter = 2( l + h)

Where;

l = 3 + h

Substitute the values

Perimeter = 2( 3 + h+ h)

expand the bracket

Perimeter = 2(3 + 2h)

Perimeter = 4h + 6

Hence, the expression is 4h + 6

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Answer:

Ryan: (100/13)(1/1,609.34)(3,600) =

17.21 miles per hour

Ryan is faster than Juan, by about 2.21 miles per hour

Given:

The function is:

\(f(x)=-4(2)^x\)

The graph of the function \(g(x)=f(x)+k\) is given.

To find:

The value of k.

Solution:

We have,

\(f(x)=-4(2)^x\)

\(g(x)=f(x)+k\)

Using these two functions, we get

\(g(x)=-4(2)^x+k\)

From the given graph it is clear that the graph of g(x) passes through the point (0,2). It means the point (0,2) satisfies the function g(x).

Substituting \(g(x)=2\) and \(x=0\) in the above function, we get

\(2=-4(2)^0+k\)

\(2=-4(1)+k\)

\(2=-4+k\)

\(2+4=k\)

\(6=k\)

Therefore, the value of k is 6.

Answer:

y = -2, 1, 4, 7 (in order)

Step-by-step explanation:

Plug in the value of x into the equation to find y.

For example for -1, plug in x as -1 into the equation.

y = 3(x) +1

y = 3(-1) + 1

y = -2

Similarly plug in the x to find the rest of the values for y.

Answer:

x = 7    y = -3

Step-by-step explanation:

x - y = 10   ⇒   x = 10 + y

Substitute  x = 10 + y  into 2x - y = 17:

2(10 + y) - y = 17

20 + 2y - y = 17

y = -3

Substitute the found value of y into x = 10 + y to find x:

x = 10 - 3 = 7

Algebra transformation

for  Graph1 f(x)=f(x)+4

for  Graph2 f(x)=-f(x-4)

for  Graph3 f(x)=f(x-7)

for  Graph4 f(x)=f(x-2)-5

In mathematics, the reflection of a graph is a transformation that produces a mirror image of the original graph across a specific line or point. The line or point across which the reflection occurs is called the axis of reflection.

Graph1

Transform the graph by +4 units in y direction.

f(x)=f(x)+4

Graph2

Transform the graph by +4 units in x direction.

f(x)=f(x-4)

Now take the reflection of graph about x axis

f(x)=-f(x-4)

Graph3

Transform the graph by +7 units in x direction.

f(x)=f(x-7)

Graph5

Transform the graph by -5 units in y direction.

f(x)=f(x)-5

Now Transform the graph by -2 units in x direction.

f(x)=f(x-2)-5

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Value is the amount of worth, importance, usefulness or benefit that a particular individual or business holds for a particular asset or idea , Option A is the right answer.

It can be defined as the worth or usefulness of an object , or the benefit some goods provide to a business or person.

Price just tells the monetary value of a business or an asset , It doesn't account for the usefulness or benefit of that to a particular individual or business.

Cost is also similar to price

Wants is the need of a business or an Individual

Value is the amount of worth, importance, usefulness or benefit that a particular individual or business holds for a particular asset or idea

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Answer: Without knowing the specifics of the loan (e.g. interest rate, payment amount), it's not possible to determine the exact percentage of the payment that goes towards principal and interest. However, we can make some general observations:

- In the early stages of a loan, most of the payment goes towards interest, with only a small percentage going towards principal.

- As the loan is paid down over time, the percentage of the payment that goes towards principal increases, while the percentage that goes towards interest decreases.

- If the interest rate is fixed, then the payment amount will be constant throughout the life of the loan, and the percentages of principal and interest will change according to the above pattern.

Given the information provided (276 payments totaling $128,616), we can't determine the exact breakdown of principal and interest. However, if we assume that the payment amount and interest rate were fixed throughout the life of the loan, we can make some general estimates.

Let's say the loan has an interest rate of 6% and a fixed monthly payment. We can use a loan amortization calculator to see how the payment is allocated between principal and interest over time. For example, if the loan amount was $100,000, the monthly payment would be $644.30, and the payment breakdown would look something like this:

- In the first payment, $500 goes towards interest and $144.30 goes towards principal (78% interest, 22% principal).

- By the 276th payment, $16.23 goes towards interest and $628.07 goes towards principal (3% interest, 97% principal).

- Based on these estimates, we can see that over time, a larger and larger percentage of the payment goes towards principal, while the percentage that goes towards interest decreases. However, without more specific information about the loan, it's not possible to give an exact answer to this question.

Step-by-step explanation:

The amount earned on average each day is $160.

From the information, James worked for 12 consecutive days, during the first 6 days, James averaged $140 per day, his average wage for the next 5 days was $175, and for the last day, he earned $205.

It should be noted that average is also the mean. This will be calculated as:

(6 × $140) + ($175 × 5) + $205 / 12

= $840 + $875 + $205 / 12

= $1920 / 12

= $160

The average amount is $160.

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The correct symbolic expression for a is option C) \(\frac{ma_{1} +F}{m}\)

A symbolic expression, also known as a mathematical expression, is a combination of numbers, variables, and mathematical operators (such as +, -, *, /) that can be evaluated to produce a numerical result.

Symbolic expressions can also contain functions, constants, and mathematical operations like logarithms, trigonometric functions, etc. They can be used to model physical phenomena or to solve mathematical problems.

A logarithmic function is a mathematical function that expresses the power (or exponent) to which a fixed number (the base) must be raised to produce a given value.

It is typically written in the form "logb(x)" where b is the base and x is the value being evaluated. The most common base used is 10 (common logarithm) or e (natural logarithm)

These expressions can be used to represent mathematical concepts, relationships, or equations.

Therefore, The correct symbolic expression for a is option C) \(\frac{ma_{1} +F}{m}\).

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Answer:

-2,1,6,13,22

Step-by-step explanation:

cn = n^2 -3

Let n=1

c1 = 1^2 -3 = 1-3 = -2

Let n=2

c2 = 2^2 -3 = 4-3 = 1

Let n=3

c3 = 3^2 -3 = 9-3 = 6

Let n=4

c4 = 4^2 -3 = 16-3 = 13

Let n=5

c5 = 5^2 -3 = 25-3 = 22

The answer is:

Work/explanation:

Bear in mind that the sum of all the angles in a triangle is 180°.

Given two angles, we can easily find the third one.

Let's call it x.

Next, we set up an equation:

\(\sf{54+87+x=180}\)

\(\sf{141+x=180}\)

Subtract 141 on each side.

\(\sf{x=180-141}\)

\(\sf{x=39}\)

1) The probabilities are given as follows:

a) More than 75: 0.0301 = 3.01%.

b) Between 60 and 73: 0.4484 = 44.84%.

c) Less than 50: 0.1057 = 10.57%.

2) The proportion of students who fail the module is of: 0.0062 = 0.62%.

3) The measures are given as follows:

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation in this problem are given as follows:

\(\mu = 60, \sigma = 8\)

The probability that an score is more then 75 is one subtracted by the p-value of Z when X = 75, hence:

Z = (75 - 60)/8

Z = 1.88

Z = 1.88 has a p-value of 0.9699.

1 - 0.9699 = 0.0301 = 3.01%.

The probability of an score between 60 and 73 is the p-valeu of Z when X = 73 subtracted by the p-value of Z when X = 60, hence:

Z = (73 - 60)/8

Z = 1.63

Z = 1.63 has a p-value of 0.9484.

Z = (60 - 60)/8

Z = 0

Z = 0 has a p-value of 0.5.

Then:

0.9484 - 0.5 = 0.4484 = 44.84%.

The probability of an score less than 50 is the p-value of Z when X = 50, hence:

Z = (50 - 60)/8

Z = -1.25

Z = -1.25 has a p-value of 0.1057.

The proportion who might fail the test is the p-value of Z when X = 40, hence:

Z = (40 - 60)/8

Z = -2.5

Z = -2.5 has a p-value of 0.0062.

Then the statistical measures are obtained as follows:

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Answer:.3

Step-by-step explanation: if it is 5 or above it rounds up

The volume of the cylinder is 169.7. (Option C)

Based on the provided information, let the radius of the cylinder be r and diameter of the cylinder be 2r. The diameter and height of the circular cylinder is the same. When examining the cross section of the cone and cylinder, there are two similar triangles. Hence,

(15 – 2r)/15 = r/5

5(15 – 2r)= 15r

75 – 10r = 15r

r = 3

Volume of the cylinder = πr^2h where r is the radius of the cylinder and h is the height of cylinder. As h = 2r, Hence,

V = πr^2(2r) = (22/7)(3^2)(6) = 169.7

Note: The question is incomplete as the options are incorrect. The correct options are A) 127.5 B) 151.6 C) 169.7 D) 168.5

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Given:

Required:

We need to factorize the given expressions.

Explanation:

The common multiple in all terms is (x+2).

Take out the common term (x+2).

Final answer:

K)

Given:

Explanation:

The given expression can be written as follows.

Final answer:

l)

Given:

Explanation:

Final answer:

To find the height of the column of water in the Fountain Hills fountain, we can use the tangent function and the information given in the problem. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side in a right triangle. In this case, we can use the angle of elevation to the top of the fountain, the distance from the surveyor to the base of the fountain, and the height of the column of water to form a right triangle.

We can then use the tangent function to find the height of the column of water as follows:

tan(29.7°) = opposite/adjacent

opposite = tan(29.7°) * adjacent

opposite = tan(29.7°) * 980 feet

opposite = 0.56 * 980 feet

opposite = 548.8 feet

Therefore, the height of the column of water in the Fountain Hills fountain is approximately 549 feet. To the nearest 10 feet, this is 550 feet.

Answer:

69.53 or 70(depending on rounding)

Step-by-step explanation:

The squares area is (9*2)^2 which is 324.

The circles area is 9^2 pi or 254.47 approx.

Subtract and you get 69.53 or 70

The simplified expression in mathematical form is -45.36.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The expression given is -

(-15 + (-1.6 + 9.34) / 6) × (3² - 5.7)

Simplifying the terms inside the parentheses first, we get -

(-15 + 7.74 / 6) × (9 - 5.7)

Next, we simplify 7.74 / 6 by dividing the numerator by the denominator -

(-15 + 1.29) × (9 - 5.7)

We add -15 and 1.29 inside the first set of parentheses -

(-13.71) × (9 - 5.7)

We subtract 5.7 from 9 inside the second set of parentheses -

(-13.71) × 3.3

Multiplying these two terms, we get -

-45.363 ≈ -45.36

Therefore, the value is obtained as -45.36.

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a) Using the standard divisors according to Jefferson's apportionment method, the number of salespeople assigned to work each shift is as follows:

Shift                              Morning     Midday     Afternoon     Evening   Total

Number of

salespeople assigned  1               3                  5                 7                16

b) The modified or adjusted divisor used represents the average number of customers for each shift divided by the standard divisor.

The standard divisor shows the ratio of the total population to the number of seats.

The standard divisor gives an insight about the number of people each seat represents.

Standard divisor = Total number of customers / Total number of salespeople

The total number of customers = 1,425

The number of salespeople = 16

a) Standard divisor = 1,425 ÷ 16

= 89.0625

Shift                              Morning     Midday     Afternoon     Evening   Total

Average number of

customers                     125            280             460             560       1,425

Standard divisor      89.0625     89.0625      89.0625      89.0625

b) Modified divisor     1.4035        3.1438          5.165           6.288

Number of

salespeople assigned  1               3                  5                 7                16

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

3520.10*7.77%= $273.51

Answer:

C. 1655

Step-by-step explanation:

+10, +4, -21, +23, -8

Adding all those terms together we get 8

1647 + 8 = 1655