The sum of a and b is obtained as follows:
a + b = 5.
How to obtain the values of a and b?The function for this problem is defined as follows:
f(x) = ax/[bx - 4]
f(1) = -2 means that when x = 1, y = -2, hence:
-2 = a/(b - 4)
a = -2b + 8
f(2) = 2 means that when x = 2, y = 2, hence:
2 = 2a/(2b - 4)
2a = 4b - 8
a = 2b - 4.
Equaling the two equations, the value of b is obtained as follows:
-2b + 8 = 2b - 4
4b = 12
b = 3.
Hence the value of a is ob:
a = 2b - 4
a = 2(3) - 4
a = 2.
Hence the sum is of:
a + b = 2 + 3
a + b = 5.
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5. 7 movie tickets for $56
To find out how much each ticket costs, we can use this equation:
Total cost ÷ Number of tickets = Price of each ticket
Inserting the numbers into the equation would look like this:
56 ÷ 7 = 8To check our work, we can multiply the number of tickets by the price of each ticket to see if it matches up to the correct total price.
7 × 8 = 56Therefore, each ticket costs $8.
Brittany works as a medical office assistant. She is married and claims 2 withholding allowances. Use the wage
bracket method to find Marianne's withholding tax if her monthly gross earnings are $3,270.
$305.00
$155.00
$205.00
$255.00
Marianne's withholding tax if her monthly gross earnings are $3,270 is $305.00.
The correct option is A.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
Brittany works as a medical office assistant.
She is married and claims 2 withholding allowances.
Her monthly gross earnings are $3,270.
So, 3270 - 2(666.5) = $1937.3
So,
(1937.3 x 0.15) + 14.49 = $305.00
Therefore, the value is $305.00.
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Ron is making dinner for his family.
The recipe he is using calls for
0.5 kilogram of ground chicken. How
many grams of ground chicken does
he need?
He need the 500 gram of ground chicken.
What is unit conversion?It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.
We are Given that the total kilogram of chicken = 0.5 kilograms
Recall :
1000 grams = 1 kilogram
Hence,
B grams = 0.5 kg
B = (0.5 x 1000) = 500 gram.
Hence,
The 500 gram of ground chicken.
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Lacey and Euan start with the same positive whole number. Lacey rounds the number to the nearest 10, and Euan rounds it to the nearest 100. Their new numbers are different to each other. Lacey's new number is 3/4 of Euan's new number. Work out a possible value for the original number.
The possible value for the original number is 30
How to determine the possible value for the original number.Represent the number with n
So, we have
Lacey = 10 * (n/10 + 1/2)
Euan = 100 * (n/100 + 1/2).
Also, Lacey's new number is 3/4 of Euan's new number, so we have:
10 * (n/10 + 1/2) = (3/4) * (100 * (n/100 + 1/2))
Solving for n, we have:
100 * (n/100 + 1/2) = (4/3) * (10 * (n/10 + 1/2))
Divide through by 100
n/100 + 1/2 = (4/30) * (n/10 + 1/2)
Evaluate
(n + 50)/100 = 4n/300 + 2/30
So, we have
n + 50 = 4n/3 + 20/3
Multiply through by 3
3n + 50 = 4n + 20
Evaluate the like terms
n = 30
Hence, the original number is 30
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Wendy's math certificate is 7 inches tall and 9 inches wide. Wendy wants to put the certificate in a fancy frame that costs $2.00 per inch. How much will it cost to frame Wendy's math certificate?
Answer:
Step-by-step explanation:
The perimeter of Wendy's math certificate is 7 inches + 7 inches + 9 inches + 9 inches = 32 inches.
So, the cost to frame Wendy's math certificate would be $2.00 per inch * 32 inches = $64.00.
Lei is designing a construction set for small children. The set includes cylindrical cups with radii of 5 cm, 6 cm, and 7 cm as well as rectangular blocks that measure 7 cm by 8 cm by 9 cm. Will the blocks fit inside all of the cups?
The rectangular blocks with the measure of 7 cm by 8 cm by 9 cm will not fit in the smallest cylindrical cup with the radius of 5cm.
Rectangular block with the least dimensions, 7cm by 8cm side.
Circle with radius r is x² + y² = r²
∴ x² + y² = 5² or x² + y² = 25
Draw the area of the block using the coordinates (3.5,4) ; (-3.5,4) ; (-3.5,-4) and (3.5,-4)
Its observed that the block cannot fit inside the cup. We can confirm this if
y >4 when x = 3.5
3.5² + y² = 25
12.25 + y² = 25
y² = 12.75
taking positive square root, y≈3.57
Since this is <4, the block cannot fit the 5 cm radius cup.
equation for the cup with r = 6cm,
x² + y² = 6² or x² + y² = 36
Draw the area of the block using the coordinates (3.5,4) ; (-3.5,4) ; (-3.5,-4) and (3.5,-4)
it is observed the block will fit inside the cup as y>4 when x = 3.5
3.5² + y² = 36
12.25 + y² = 36
y² = 23.75
taking positive square roots, y≈4.87
Since this is >4, the block can fit the 6 cm radius cup.
equation for the cup with r = 7cm,
x² + y² = 7² or x² + y² = 49
Draw the area of the block using the coordinates (3.5,4) ; (-3.5,4) ; (-3.5,-4) and (3.5,-4)
it is observed the block will fit inside the cup as y>4 when x = 3.5
3.5² + y² = 49
12.25 + y² = 49
y² = 36.75
taking positive square roots, y≈6.06
Since this is >4, the block can fit the 7 cm radius cup.
∴ the block will not fit the smallest cup
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what chart should be used if all the sample sizes are the same and the team is concerned with the number of defects?
A bar chart or a histogram might be suitable if all the sample sizes are the same and the team is worried about the amount of flaws.
You might compare the number of problems between various categories or groups using a bar chart.Consider comparing the quantity of defects across several production lines, departments, or time periods.
Similar to a bar chart, a histogram displays the frequency distribution of a continuous quantity rather than particular categories.The number of faults would be the continuous variable in this instance, and the bars would represent the number of samples that included a particular number of defects.
When illustrating the distribution of a count variable, such as the number of defects, bar charts and histograms can be used to visually spot patterns and trends in the data.
Therefore, the number faults would be the continuous variable in this instance, and the bars would represent the number of samples that included a particular number of defects.
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a rectangle has a width-to-height ratio of 8:5. The perimeter of the rectangle is 208 inches. what is that area of the rectangle, in square inches?
The dimension of the rectangle is 40 inches by 64 inches. Then the area of the rectangle is 2,560 square inches.
What is the area and perimeter of the rectangle?Assume L is the length and W is the width. Then the area is given as,
A = L × W
And the perimeter is given as,
P = 2(L + W)
A rectangle has a width-to-height ratio of 8:5. The perimeter of the rectangle is 208 inches. Then the equations are given as,
208 = 2(W + H)
H + W = 104 ...1
H / W = 8 / 5 ....2
From equations 1 and 2, then we have
(8/5)W + W = 104
(13/5)W = 104
W = 40 inches
Then the height is given as,
H = (8/5) x 40
H = 64 inches
Then the area of the rectangle is given as,
A = 40 x 64
A = 2,560 square inches
The dimension of the rectangle is 40 inches by 64 inches. Then the area of the rectangle is 2,560 square inches.
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Pls help me on this math equation
Step-by-step explanation:
This is a trick question I think.
It says he managed to only travel 3 7/8. So wouldn't that mean the fraction of his planned trip that he travel would be... 3 7/8? Unless they want it as 31/8? Something is odd with the question
Are x and y common factors?
Answer:
yes
Step-by-step explanation:
In maths, x and y are variables. common factor is taken only when these variables are repeatedly used.
Keisha collects vintage glass marbles. Her favorite marbles have a diameter of 2.5 centimeters each. She keeps 66 of her favorite marbles in a pouch. One cubic centimeter of glass has a mass of 2.6 grams. What is the mass of the marbles in Keisha’s pouch rounded to the nearest gram? Use 3.14 for π
Answer:
The volume of one marble can be calculated as follows:
V = (4/3) * π * (r^3)
where r = 1.25 cm (diameter of 2.5 cm divided by 2)
V = (4/3) * 3.14 * (1.25^3) = 5.20 cm^3
The mass of one marble is then:
m = V * 2.6 g/cm^3 = 13.52 g
And the total mass of 66 marbles is:
m = 66 * 13.52 g = 888.32 g
Rounding to the nearest gram, the total mass of the marbles in Keisha's pouch is 888 g.
it is believed that 85% of all individuals love bts. we took a sample of 30 individuals and found the 95% of all people love bts. what is the z score associated with our observation (round answers to two decimal places)?
The Z score associated with our observation is 2.45. This means that our observed value is 2.45 standard deviations away from the expected value.
2.45
Z score = (Observed value - Expected value) / Standard Deviation
Z score = (95 - 85) / √(85*(1-85)/30)
Z score = 2.45
We can calculate the Z score associated with our observation by taking the observed value, 95%, and subtracting the expected value, 85%, and dividing this by the standard deviation. To calculate the standard deviation, we use the formula: √(expected value*(1-expected value)/sample size). In this case, 85*(1-85)/30. The Z score associated with our observation is 2.45. This means that our observed value is 2.45 standard deviations away from the expected value.
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Write the following as a composition of two or more non-identity functions.
(2x^3 + 2)/(x^3 - 2)
The given expression (2x^3 + 2)/(x^3 - 2) can be written as a composition of two non-identity functions as follows:
Let f(x) = 2x^3 + 2 and g(x) = x^3 - 2.
Then, the expression can be written as:
f(x)/g(x) = (2x^3 + 2)/(x^3 - 2)
So, the expression is a composition of the two non-identity functions f and g, written as:
h(x) = f(g(x)) = (2x^3 + 2)/(x^3 - 2)
a bag contains four red jelly beans and 7 green jelly beans. what is the probability of randmly wuthdrawing 5 jellybeans such that at least 2 are red
To find the probability of randomly withdrawing 5 jellybeans such that at least 2 are red, we need to find the total number of ways to select 5 jellybeans from the bag and then find the number of ways to select 2 or more red jellybeans.
Let's first find the total number of ways to select 5 jellybeans from the bag:
Total number of jellybeans = 4 red + 7 green = 11 jellybeans
Number of ways to select 5 jellybeans from 11 = 11 choose 5 = 462
Next, we need to find the number of ways to select 2 or more red jellybeans:
Number of ways to select 2 red jellybeans = 4 choose 2 = 6
Number of ways to select 3 red jellybeans = 4 choose 3 = 4
Number of ways to select 4 red jellybeans = 4 choose 4 = 1
Total number of ways to select 2 or more red jellybeans = 6 + 4 + 1 = 11
The desired probability is the ratio of the number of favorable outcomes (selecting 2 or more red jellybeans) to the total number of possible outcomes (selecting 5 jellybeans):
P(at least 2 red) = 11/462 = 11/462 = 0.0239 or 2.39%
So, the probability of randomly withdrawing 5 jellybeans such that at least 2 are red is 2.39%.
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help plssssssssssssssss
•Mr Bradford lunged at his wedding ring as it fell into the WHIRLPOOL of the bathtub drain.
•Sarah's morher CALMED her screaming baby by giving her a teddy bear to hold.
Answer: whirlpool, calmed
Step-by-step explanation:
A vortex looks like a whirlpool
Since the baby is scream giving a teddy bear will probably calm it
The price of a $198.00 smart phone is discounted 40% for a special promotion. What is its sale price during the promotion?
Practice
Think about if the sale price will be more or less than $198.00.
Answers:
A
$190.08
B
$120.80
C
$118.80
D
$79.20
Say someone answered D how would someone get that answer? (inocorrect math explain)
Answer:
the answer is c
Step-by-step explanation:
Divide 198.00 by 100, multiply 1.98 by 40, 198.00 minus 79.20, 118.80
What scale factor was applied to the first diamond to get the resulting image?
(21 points)
The scale factor was applied to the first diamond is 2.5
How to determine the scale factorFrom the question, we have the following parameters that can be used in our computation:
The diamonds
The scale factor is calclated as
scale factor = Diamond 2/Diamond 1
Substitute the known values in the above equation, so, we have the following representation
scale factor = 1.5/0.6
Evaluate
scale factor = 2.5
Hnce, the scale factor is 2.5
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The number of fish on a fish farm increases by approximately 10% each month. If there were originally 350 fish, calculate to the nearest 100 how many fish there would be after 12 months.
Answer:
There would be 600 fish after 12 months.
Step-by-step explanation:
The number of fish on the farm increases by 10% each month, so the formula to calculate the number of fish after n months is:
F = 350 * (1 + 0.1)^n
where,
F is the number of fish after n months
We want to find the number of fish after 12 months, so:
F = 350 * (1 + 0.1)^12
F = 350 * 1.719178
F = 603.56 to the nearest 100, which is 600.
A soccer game is m minutes long. The game includes 90 minutes plus x minutes of time-outs. Translate the words into an algebraic expression. How long is the game with 8 minutes of time-outs
The game with 8 minutes of time-outs is 98 minutes long.
What is an algebraic expression?
An algebraic expression is a mathematical phrase that can contain numbers, variables, and operations such as addition, subtraction, multiplication, and division.
In this case, the algebraic expression that represents the length of the soccer game would be:
m = 90 + x
where m represents the total length of the game in minutes, 90 represents the fixed length of the game, and x represents the variable length of time-outs in minutes.
To find the length of the game with 8 minutes of time-outs, we substitute x = 8 into the expression:
m = 90 + 8 = 98
Therefore, the game with 8 minutes of time-outs is 98 minutes long.
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Which expression has a solution of 12, if m = 7?
Answer:
“m + 5”
internet
I HAVE 10 MINUTES PLEASE HELP!!!!The density of water is 1 gram per cubic centimeter. An object floats in the water if its density is less than water's density, and it sinks if its density is great than water's.
Suppose a ball with mass 90 grams is in the shape of a sphere with radius 4 centimeters. Will the ball sink or float in the water?
ROUND YOUR ANSWERS TO THE NEAREST HUNDRETH AND USE THE
π
π
BUTTON WHEN CALCULATING
The volume of the ball is about___cubic centimeters. The density of the ball is___grams per cubic centimeter. Based on its density, the ball will___.
Answer:
Step-by-step explanation:
Basically, we want to use the formula for the area of a sphere: V = 4/3πr^3
And plug-in our radius, 4 for r.
We get an answer around 67 sooooooo
The volume of the ball is about__67__cubic centimeters. The density of the ball is__1.343__grams per cubic centimeter. Based on its density, the ball will__sink__.
Answer:
The base should be sink
Calculation of the volume, density:
Since the density of water is 1 gram per cm^3.
The volume is
Here a = base area and h = height of the pyramid
So,
Now
Density is
Since The mass of the pyramid is 1.17 g.
So, the density is
Density
Since its density is more than that of water, so it will sink.
Hence, we can conclude that The base should be sink.
Step-by-step explanation:
Hope this helped!
need help with this question
The total expenditure of a company can be broken down as follows: Salaries: R105 000 000 Equipment: R10 000 000 Marketing: R2 000 000 Other: R8 000 000 What percentage of the expenditure goes towards salaries?
The percentage of expenditure which goes towards salaries is 78%
What percentage of the expenditure goes towards salaries?Company's expenditure:
Salaries: R105 000 000
Equipment: R10 000 000
Marketing: R2 000 000
Other: R8 000 000
Total expenditure= R105 000 000 + R10 000 000 + R2 000 000 + R8 000 000
= R135,000,000
percentage of the expenditure is salary= R105 000 000 / R135,000,000 × 100
= 0.78
= 78%
Therefore, 78% of the company's expenditure goes towards salary.
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HELP ME PLS I NEED HELP RN
Answer:
Step-by-step explanation:
I gotchu.
sin70 = x/3.6
x = 3.6sin70
x = 3.4
Answer:
x = 3.4
Step-by-step explanation:
As the given triangle is a right triangle we can use trigonometric ratios to solve for x.
[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
From inspection of the triangle:
θ = 70°O = AB = xA = BCH = AC = 3.6As we know the angle and the hypotenuse, and wish to find the side opposite the angle, substitute the values into the sine ratio and solve for x:
[tex]\implies \sin(70^{\circ})=\dfrac{x}{3.6}[/tex]
[tex]\implies x=3.6\sin(70^{\circ})[/tex]
[tex]\implies x=3.382893...[/tex]
[tex]\implies x=3.4\; \sf (nearest\;tenth)[/tex]
Therefore, x = 3.4 to the nearest tenth.
Genesis is trying to pick out an outfit for the first day of school. She can choose from 7 pairs of pants, 2 t-shirts, 3
sweaters or hoodies, and 3 pairs of shoes. How many
different outfits does Genesis have to choose from?
Help please
Answer:
Genesis has 126 different outfits to choose from.
Step-by-step explanation:
To calculate the total number of different outfits Genesis can choose, we need to multiply the number of choices available for each article of clothing. So we have:
7 choices for pants
2 choices for t-shirts
3 choices for sweaters or hoodies
3 choices for shoes
To find the total number of outfits, we multiply the number of choices for each category:
7 x 2 x 3 x 3 = 126
Therefore, Genesis has 126 different outfits to choose from.
126 different combination does Genesis have to choose.
We have,
Pants = 7
T shirts = 2
Sweaters or Hoodies = 3
Shoes = 3
So, the number of different combination is
= C(7, 1) x C( 2, 1) x C(3, 1) x C(3, 1)
= 7 x 2 x 3 x 3
= 126 ways
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Two model cars, A and B, are in a race.
They start together on the starting line.
Assume each car travels at a constant speed.
Car A takes 30 seconds to complete each lap of the track.
Car B takes a whole number of seconds to complete each lap of the track.
The two cars next cross the starting line together 150 seconds after the start of the race.
Find the four possible times that car B could take to complete one lap.
The four possible times that car B could take to complete one lap are: 120 seconds, 90 seconds, 60 seconds, and 30 seconds.
The equation used to solve this problem is (150 - 30) = N * B, where N is the number of laps and B is the total number of seconds for car B to complete one lap. Therefore, the four possible times for car B to complete one lap are 120 seconds, 90 seconds, 60 seconds, and 30 seconds.
When solving for the total time, it is important to remember that the two cars start the race together and that their speeds remain constant. This means that the time it takes for car B to complete one lap must be a factor of 150 seconds. If car B takes a time that is not a factor of 150, then it will not be able to finish the race in 150 seconds.
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(a) in how many ways can 3 boys and 3 girls sit in a row? (b) in how many ways can 3 boys and 3 girls sit in a row if the boys and the girls are each to sit together? (c) in how many ways if only the boys must sit together? (d) in how many ways if no two people of the same sex are allowed to sit together?
a) 720 ways 3 boys and 3 girls sit in a row.
b) 48 ways boys and the girls are each to sit together.
c) 6 ways boys must sit together.
What is Combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.
Given:
Number of girls= 3
Number of boys = 3
a) Using Permutation
⁶P₆ = 6! / (6 - 6)!
⁶P₆ = 6! / (0!)
⁶P₆ = 6!
= 6 × 5 × 4 × 3 × 2 × 1
= 30 × 24
= 720
b) 3 boys and 3 girls sit in a row if the boys and the girls are each to sit together
= 3! x 2³
= 3 x 2 x 2 x 2 x 2
= 48 ways
c) the number of ways boys can sit together
= 3!
= 6 ways
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Write the expression 15^1/2 in radical form.
Answer:
15
_
2
Step-by-step explanation:
hope you get it since I don't know how to do it under __
Which other expression has the same value as (-14)-8