Answer:
The 5th row has 24 chairs, and therefore not enough chairs for 100 people.
Step-by-step explanation:
The equation for this situation is , f(x) = 4x+4 The reason for this is, there is 4 chairs added to every row, so in order to make row number one make sense, you must subtract 4 to find the y-intercept which is also 4.
To find if the 5th row has enough for 100 people, you must plug 5 in for x
The 5th row has 24 chairs, and therefore not enough chairs for 100 people.
The required chairs in the 5th row there is 24 chairs and 5 rows are not enough to accommodate 100 people.
What is arithmetic progression?Arithmetic progression is the series of numbers that have common differences between adjacent values are common.
Here,
A given scenario is of arithmetic progression,
Let the first term be a = 8,
and the common difference between chairs is d = 4,
Now,
Let the number of rows be n,
Now,
The explicit arithmetic formula is given as,
Number of chairs = 8 + (n - 1)4
Now put n = 5
Number of chairs = 8 + (5 - 1) 4
= 8 + 16
= 24
So, in the 5th row, there will be 24 chairs.
Now,
For 100 people number of chairs would be 100
Apply the sum formula of arithmetic progression,
Where sum gives the total number of chairs for n rows,
Sum = n / 2 (a + l)
Sum = 5 / 2(8 + 24)
= 5 / 2 (32)
= 5 × 16
= 80 chairs
Thus, the required chairs in the 5th row there is 24 chairs and 5 rows are not enough to accommodate 100 people.
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Find the value of x *
2x - 12
2
1
3
This is triangle proportional theorem and I need help
Answer:
2x2+1+3-12
4+1+3-12
5+3-12
8-12
-4x
Using technology, determine the present value given that you make quarterly payments of $1,635 at 4.2% compouded quarterly over a 3 year period. Round your answer to the nearest cent. a. $15,168.06 c. $19,180.84 b. $19,188.94 d. $18,344.05
Present value of the quarterly payments of $1,635 at 4.2% compounded quarterly over a 3 year period is $18,344
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
The present value of the quarterly payments of $1,635 at 4.2% compounded quarterly over a 3 year period is calculated as follows:
Present Value = $1,635 × PVIFA ( 4.2%/4 ,3 Years)
Present Value = $1,635 × PVIFA (1.05% ,12)
= $1,635 × 11.21960
= $18,344
The present value of the quarterly payments of $1,635 at 4.2% compounded quarterly over a 3 year period is $18,344
Hence, present value of the quarterly payments of $1,635 at 4.2% compounded quarterly over a 3 year period is $18,344
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Social Security tax: 6.2%. Maximum: $106,800. Medicare tax: 1.45%
In 2009, Dr. Kirmser's gross pay was $381,318.60.
What was her monthly gross pay?
Dr. Kirmser's monthly gross pay = $ 29345.65
Social Security tax:Employers and workers are both subject to the Social Security tax, which is used to pay for the country's Social Security program. Federal Insurance Contributions Act (FICA)-mandated payroll taxes or Self-Employed Contributions Act-mandated self-employment taxes are the two ways that Social Security tax is collected (SECA).
Here we have
In 2009, Dr. Kirmser's gross pay was $381,318.60.
Social Security tax = 6.2% [ Maximum: $106,800 ]
=> 6.2% = 6.2/100 = 0.062
Medicare tax = 1.45%
=> 1.45% = 1.45/100 = 0.0145
From the above information,
Total tax on salary =0.062 + 0.0145 = 0.0765
In 2009, Dr. Kirmser's gross pay was $381,318.60.
Tax can be calculated on Gross pay = 0.0765 × $381,318.60
= 29170.827
As we know
Net pay = gross salary - deductions
=> Monthly gross pay = $381,318.60 - $29170.827 = $ 352147.773
Therefore,
Dr. Kirmser's monthly gross pay = 352147.773 ÷ 12 = $ 29345.65
Hence,
Dr. Kirmser's monthly gross pay = $ 29345.65
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how do you subtract mixed fractions?
Answer: Making them into improper fractions will really help you with subtracting mixed fractions! For example 2[tex]\frac{1}{5} \\[/tex] - 1[tex]\frac{1}{4}[/tex].
Making them into improper fractions will turn the expression into [tex]\frac{11}{5}[/tex] - [tex]\frac{5}{4}[/tex].
Turn the denominators into the greatest common multiple, so the greatest common multiple of 5 and 4 is 20. Meaning you multiply [tex]\frac{11}{5}[/tex] by 4 and [tex]\frac{5}{4}[/tex] by 5.
You now have [tex]\frac{44}{20} -\frac{25}{20}[/tex], which is much easier to work with. Simply subtract the numerators, and you should get [tex]\frac{19}{20}[/tex].
Hope this helps :)
Use two unit multipliers to convert 300 inches to meters.
Answer: 7.62m
Step-by-step explanation:
[tex]300in(\frac{2.54cm}{1in})( \frac{0.01m}{1 cm} )[/tex]
[tex]7.62m[/tex]
What is the intermediate step in the form (x+a)^2=b(x+a) 2 =b as a result of completing the square for the following equation? x^{2}+32x+116= x 2 +32x+116= \,\,12x 12x
The intermediate step of equation x^{2}+32x+116=0 is (x + 16)² = 140
In this question, we have been given an equation x^{2}+32x+116=0
We need to find the intermediate step in the form (x + a)^2=b as a result of completing the square for the given equation
We can write given equation as,
x^{2}+32x= -116
Take the coefficient of x
k = 32
Divide it by 2
k/2 = 16
Square both sides
(k/2)^2 = 256
Add 256 to both sides of x² + 32x = -116
x² + 32x + 256 = -116 + 256
(x + 16)² = 140
Therefore, the intermediate step of equation x^{2}+32x+116=0 is (x + 16)² = 140
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Find the percentage error of the mass of a bag of sugar that weighs 10.00kg, correct to 2 decimal places.
The percentage error of the mass of a bag of sugar that weighs 10.00kg is 0.1%
The mass of a bag of sugar that weighs = 10.00 kg
The possible error measurements are 10.01, 10.02 etc
The least count error in the measurements = 0.01
The percentage of error = (The least count error in the measurements / The mass of a bag of sugar that weighs ) × 100
Substitute the values in the equation
The percentage of error = (0.01 / 10) × 100
Divide the terms
= 0.001 × 100
Multiply the terms
= 0.1%
Hence, the percentage error of the mass of a bag of sugar that weighs 10.00kg is 0.1%
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GCF (96,144).............................
Answer:
The LCM of 96 and 144 is 288.
Step-by-step explanation:
Please give the brainliest, really appreciated.
If Q(t)= C/4t - 1 an equation for Q-¹(t) is
If Q(t)= C/4t - 1 an equation for Q-¹(t) is y = C + t/4t.
Define equation.A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.
Given,
Q(t) = C/4t -1
Put a "y" in place of the "Q(t)":
y = C/4t -1
Change the t and y since each (t, y) has a corresponding (y, t) companion.
t = C/4y -1
Distribute t by multiplying into the bracket to find y.
t × 4y -1 = C
t × 4y - t = C
Add both sides of the equation together now.
t × 4y = C +t
4t divided by both sides
y = C + t/4t
If Q(t)= C/4t - 1 an equation for Q-¹(t) is y = C + t/4t.
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this picture will answer a question. Question: During what interval(s) of the domain is the baseballs height increasing?
(btw you have to write the answer, there is no multiple choice)
Answer:
(0,2)
It increases at the beginning. From 0 to 2 on the x axis
Solve for Y. X=2/3(Y+Z)
Y=3X/2-Z for the equation X=2/3(Y+Z)
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is
X=2/3(Y+Z)
x equal to two by three times of y plus z
Apply distributive property on RHS
X=2Y/3+2/3Z
Now Subtract 2/3Z on both sides
X-2/3Z=2/3Y
Divide both sides by 2/3
3/2X-Z=Y
Hence Y=3X/2-Z for the equation X=2/3(Y+Z)
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
16/9, 4/3, 1, 3/4, and 9/16
Step-by-step explanation:
1.) Plug these x values into the equation. You will get: 16/9, 4/3, 1, 3/4, and 9/16.
Answer:
16/9, 4/3, 1, 3/4, and 9/16
Step-by-step explanation:
1.) Plug these x values into the equation. You will get: 16/9, 4/3, 1, 3/4, and 9/16.
Noreen can walk 13 mile in 12 minutes. What is her average speed in miles per hour?.
The average speed in miles per hour is 1.67 miles/hour
What is her average speed?
Average speed is calculated by dividing distance by time (eg miles/hour).
Given that, Noreen can walk 1/3 mile in 12 minutes.
We need to find her average speed.
We know that the total distance covered divided by the total time taken is called the average speed of Noreen.
Mathematically, it is given by :
v=d/t
t = 12 minutes = 0.2 hours
v=(1/3 mile)/0.2 hours
v = 1.67 miles/hour
So, the average speed of Noreen is 1.67 miles/hour. Hence, this is the required solution.
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The graph shows the distance traveled by an Olympic-level sprinter over time during a race.
Find the slope of the line, and complete the sentences below.
100 meter race graph of a diagonal line on a coordinate plane going up and to the right with Time in seconds on the x axis and Distance in meters on the y axis. The line begins at the origin and passes through the point 2 comma 20.
The slope of the line is 10.
Given:
The graph shows the distance traveled by an Olympic-level sprinter over time during a race.
The line begins at the line begins at the origin and passes through the point (2,20).
slope between (0,0) and (2,20).
slope m = y2 - y1 / x2 - x1
= 20 - 0 / 2 - 0
= 20/2
= 10.
Therefore the slope of the line is 10.
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The price of an item yesterday was $80. Today, the price rose to $216. Find the percentage increase.
Answer:
170%
Step-by-step explanation:
increase in price = 216 - 80 = $136
x : 100 = 136 : 80
x = 100 * 136 / 80
x = 10 * 136/8
x = 1360 / 8
x = 170 %
Answer:
170%
Step-by-step explanation:
80+170%=$216
consider the function f(x) =3x+8, What is the correct set up for f(x)=7?
Answer: 29
Step-by-step explanation: 3 times 7 = 21 + 8 = 29
Answer:
7=3x+8
x=-1/3
Step-by-step explanation:
we just replace f(X) with 7
7=3x+8
-8. -8
-1=3x
/3. /3
-1/3=x
Hopes this helps please mark brainliest
Harper needs to mail an envelope. She weighs it at home as 10.4 ounces. When she gets to the post office, the clerk weighs it at 9.6 ounces. What is the percent error in the weight of the envelope
The percent error in the weight of the envelope is 7.69%.
What is the percentage?Given that Harper weighs it at home as 10.4 ounces and then when she gets to the post office, the clerk weighs it at 9.6 ounces.
The percentage error will be:
= Change in value / Original value × 100
= (10.4 - 9.6) / 10.4 × 100
= 0.8 / 10.4 × 100
= 7.69%
The percentage is 7.69%.
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13. LMN-QMP. Find the length of LM
Answer:
LM = 18
Step-by-step explanation:
since the triangles are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{LM}{QM}[/tex] = [tex]\frac{LN}{QP}[/tex] ( substitute values )
[tex]\frac{LM}{12}[/tex] = [tex]\frac{15}{10}[/tex] ( cross- multiply )
10 LM = 180 ( divide both sides by 10 )
LM = 18
An artist used 6 tubes of red paint, 2 tubes of yellow paint, 13tubes of white paint, and 9 tubes of blue paint for a mural.
What is the ratio of tubes of blue paint to all of the tubes of paint used?
The ratio of tubes of blue paint to all of the tubes of paint used is 3/10
In this question, we have been given an artist used 6 tubes of red paint, 2 tubes of yellow paint, 13 tubes of white paint, and 9 tubes of blue paint for a mural.
Total number of the tubes of paint used = 6 + 2 + 13 + 9
= 30
the ratio of tubes of blue paint to all of the tubes of paint used would be,
9/30 = 3/10
Therefore, the ratio of tubes of blue paint to all of the tubes of paint used is 3/10
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what is
9e-7=7e-11
e=?
Answer:
-2
Step-by-step explanation:
9e-7=7e-11
9e-7e= -11+7
2e= -4
e= -4÷2
e= -2
7 girls : 2 boys is equivalent to what ratio?
Answer:7:2 or 7 to 2
Step-by-step explanation:
Answer:
7 : 2 7/2 we can use two
Step-by-step explanation:
7 : 2 can't simplified
The beta for the DAK Corporation is 1.25. The yield on 30-year T-bonds is 5.65 percent, and the long-term average return on the S&P 500 is-11 percent. Calculate the required rate of return for DAK Corporation. I
The required rate of return for DAK Corporation is 12.34%.
What is the required rate?
The minimal profit (return) an investor will seek or expect in exchange for taking on the risk of investing in a stock or other type of security is known as the required rate of return (RRR). RRR can also be used to determine a project's potential profitability in relation to its funding costs.
Here, we have
Given Information
Beta = 1.25
The yield on 30-year T bonds (rf)= 5.65%
Return on S&P (rM) = 11%
Required Return for DAK = rf + Beta*(rM - rf)
= 5.65% + 1.25*(11% - 5.65%)
= 12.34%
Hence, the required rate of return for DAK Corporation is 12.34%.
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When abram was born, his parents put $2,000 into an account that yielded 1. 2% interest, compounded semi-annually. When he turns 16, his parents will give him the money to buy a car. How much will abram receive on his 16th birthday?.
In linear equations, $ 309.914 will abram receive on his 16th birthday .
What are examples of linear equations?
An equation with only one variable is referred to as a linear equation in one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with just one possible value. A linear equation in one variable would be 9x + 78 = 18, for instance.Let “M” be amount of money in account.
Let “y” be number of full years passed.
1.2/2 = 0.6(%) - interest for every 6 months
y = 16
Money in the account in 16 years:
M = 2,000(1.006)2y
= 2,000(1.06)32
= 2000 * 0.154957
= $ 309.914
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Points G (-5,-8) and H (3,7) are plotted on a coordinate grid. Point J is plotted so that GH is the hypotenuse of the right triangle formed by joining the three points. What are the coordinates of point J? Select all that are possible.
(-3,-8)
(5,-7)
(-3,8)
(-5,7)
(3,8)
(5,7)
(-5,-7)
(3,-8)
(question 5.)
The coordinates of point J so that GH is the hypotenuse of the right triangle formed by joining the three points will be (3,-8).
What is a right-angle triangle?It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
Given is a coordinate grid with the points G (-5, -8) and H (3, 7) plotted on it. In order for GH to be the hypotenuse of the right triangle created by joining the three points, point J is plotted.
Thus, the coordinates of point J so that GH is the hypotenuse of the right triangle formed by joining the three points will be (3,-8).
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Factor the expression 16a4 − b4 using the polynomial identity (x2 − y2) = (x − y)(x + y)
The factorization of given expression would be,
(4a^2)^2 - (b^2)^2= (4a^2 + b^2)(4a^2 - b^2)
In this question, we have been given an expression 16a^4 − b^4
We need to factor given expression using the polynomial identity
(x^2 - y^2) = (x − y)(x + y)
We write given expression as,
16a^4 − b^4 = (4a^2)^2 - (b^2)^2
Using the above polynomial identity,
16a^4 − b^4
= (4a^2)^2 - (b^2)^2
= (4a^2 + b^2)(4a^2 - b^2)
Therefore, the factorization of given expression would be,
(4a^2)^2 - (b^2)^2= (4a^2 + b^2)(4a^2 - b^2)
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HELP ASAP!!!!!!
In this situation, simple interest is calculated yearly.
How much interest was earned?
Principal: $8000
Time: 4 years
Interest rate: 12%
The simple interest accumulated on the principal at 12% rate for 4 years is $3,840.
How to determine interest accumulated?Simple interest formula is expressed as;
I = P × r × t
Where I is interest, P is principal, r is interest rate and t is time.
Given the data in the question;
Principal P = $8000Elapsed time t = 4 yearsInterest rate r = 12%Interest I = ?First, convert the interest rate from percent to decimal.
Interest rate r = 12%
Interest rate r = 12/100
Interest rate r = 0.12
Plug the given values into the above formula and solve for interest I.
I = P × r × t
I = $8000 × 0.12 × 4
I = $3,840
Therefore, the interest earned is $3,840.
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Work out the area Give your answer in cm² and give any decimal answers to 1 d.p.
53 cm
28 cm
The triangle's surface area is 630 cm²
What is the Pythagorean theorem in plain English?
Pythagoras' Theorem states that the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. The Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides.
Given that
hypotenuse is 53 cm
base is 28 cm
and it is a right angle triangle
Area = 1/2 x Base x height
So by using Pythagorean theorem we can find its height
Height² + Base² = Hypotenuse²
Height² + 784 = 2809
Height² = 2024
Height = 45 cm
Area = 1/2 x 28 x 45
Area = 630 cm²
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true or false? there are in total 24 ways to arrange 2 out of 5 books (a, b, c, d, and e) on a shelf, if the order of each arrangement does matter.
Answer:True
Step-by-step explanation:
You have 2 different savings accounts. For Account A, the simple interest earned after 9 months is $6.94. For
Account B, the simple interest earned after 33 months is $39.60. If the interest rate is 3.7% for Account A and 2.4% for
Account B, how much is the principal in each account? Which account earned you the most interest the first month? Explain
The principal amount in account A was $250.09 and in account B it was $600.
Account B earned you the most interest the first month because $1.2 is higher than $0.7711.
What is the simple interest?
Simple interest is a quick and easy way to calculate the interest charge on a loan. Simple interest is calculated by multiplying the daily interest rate by the principal by the number of days between payments.
The formula for simple interest is expressed as
I = PRT/100
Where, P = the principal or initial amount of money invested.
R = interest rate
T = time
On account A,
I = $6.94
R = 3.7%
T = 9 months = 9/12 = 0.75 years.
Using the formula:
I = PRT/100
[tex]6.94 = \frac{P(3.7)(0.75)}{100} \\\\6.94 = 0.02775P\\\\P=250.09[/tex]
On account B,
I = $39.60
R = 2.4%
T = 33 months = 33/12 = 2.75 years
Using the formula:
I = PRT/100
[tex]39.60= \frac{P(2.4)(2.75)}{100} \\\\39.60 = 0.066P\\\\P=600[/tex]
To find the account that earned more interest in the first month we have to divide the interest by the number of months.
For account A,
6.94/9 = $0.7711
For account B,
39.60/33 = $1.2
Hence, the principal amount in account A was $250.09 and in account B it was $600.
Account B earned you the most interest the first month because $1.2 is higher than $0.7711.
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if a person usually ate 2 ounces of lean meat at lunchtime and decided to substitute cooked lentils instead, how much of the lentils would the person need to eat?
If a person substitutes 2 ounces of lean meat by cooked lentils, the lentils that the person need to eat is ½ cup as both are protein.
Lean meat and lentils are among the sources of proteins in the food intake. Protein is found throughout the human body such as in muscle, skin, hair, bone, skin, hair, and every other body part or tissue. It manufactures the enzymes that power chemical reactions and the hemoglobin that carries oxygen in your blood. Protein is required by the body to help your body repair and make new cells. The foods that contain high content of proteins include lean meat, eggs, dairy products, lentils, etc. A half cup of cooked lentils provides 9 grams of protein, and 2 ounces of lean meat provides 8 grams of proteins. As the amount of protein provided by both is similar, a person can substitute one with another and maintain their protein intake.
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