Step-by-step explanation:
Given
12a - 8 - 5a + 12
= 7a + 4
Hope it will help :)
Answer:
7a + 4
Step-by-step explanation:
First, let's rewrite this expression to combine like terms:
12a – 8 – 5a + 12 — I bolded the constants and underlined the expressions with variables
12a – 5a – 8 + 12 — it looks a little easier regrouped, doesn't it?
The last two terms are easy, right?
12 – 8 = 4 — simplify with subtraction
We'll focus on the first two terms now. Let's rewrite the terms with variables attached to make the subtraction easier:
a(12 – 5) = a(7) = 7a
We could also think of it this way: multiplication is just repeated addition.
12a = a + a + a + a + a + a + a + a + a + a + a + a (we just add a to itself 12 times)
5a = a + a + a + a + a (we just add a to itself 5 times)
Subtracting this expression would then look like this:
a + a + a + a + a + a + a + a + a + a + a + a – (a + a + a + a + a)
a + a + a + a + a + a + a + a + a + a + a + a – a – a – a – a – a
Five of the a values will cancel out, and to show this, we can rewrite the expression once more, like this:
a – a + a – a + a – a + a – a + a – a + a + a + a + a + a + a + a
The five a values cancel out and leave us with this:
a + a + a + a + a + a + a
How many a values are added together now? Seven of them, right? We add a to itself 7 times. We can then rewrite that expression as 7a.
Using the [12 – 8 = 4] expression from above, we add the 4 to the 7a to find our final answer: 7a + 4
I hope this helps increase your understanding of the concept! Have a great day!
2. Some bags of Joe Coffee coffee beans include a collectable card of one of the cute members from BTS.
inside the bag. Joe Coffe Company claims that a collectable card can be found in 20 percent of the coffee
bags. However, based on their experiences making and drinking coffee at home, Mr. Brenes and his coffee
club believes that the proportion of coffee bags with collectable cards is less than 0.2. The coffee club
purchased 65 bags of Joe Coffee coffee beans to investigate the company's claim. The coffee club found a
total of 11 collectable cards in the 65 coffee bags.
Suppose it is reasonable to assume that the 65 coffee bags purchased by Mr. Brenes and his coffee club are
a random sample of all Joe Coffee bags of coffee beans. Based on this sample, is there support for the coffee
club's belief that the proportion of bags with collectable cards is less than 0.2 ? Provide statistical evidence-
to support your answer.
The coffee club's assertion that the percentage of bags containing collectible cards is less than 0.2 is unsupported by sufficient data.
How to determine statistical evidence?To test whether the coffee club's belief that the proportion of bags with collectable cards is less than 0.2 is supported by the sample, conduct a hypothesis test.
Null Hypothesis: The proportion of bags with collectable cards is equal to or greater than 0.2.
Alternative Hypothesis: The proportion of bags with collectable cards is less than 0.2.
Let p be the true proportion of bags with collectable cards in all Joe Coffee bags. Use a one-sample proportion test to test this hypothesis.
The test statistic is calculated as follows:
z = (p - p₀) / √(p₀(1-p₀)/n)
where p = sample proportion (11/65), p₀ = hypothesized proportion (0.2), and n = sample size (65).
Using a significance level of 0.05, the critical z-value for a one-tailed test is -1.645.
Calculating the test statistic:
z = ((11/65) - 0.2) / √(0.2(1-0.2)/65) = -1.469
Since -1.469 is not less than -1.645, we fail to reject the null hypothesis. There is not enough evidence to support the coffee club's belief that the proportion of bags with collectable cards is less than 0.2.
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Ace Autos sell cars and pay Sue each month as follows.
• a salary of £1410
• 26% of the total profit the company makes from her sales
• a £390 bonus if she sells at least 16 cars
The table shows information about the cars she sold last year.
Total cost to the
Total income for
Number of months when she
company
the company
sold at least 16 cars
£473 500
£549 000
4
Work out Sue's total pay for the year.
Sue's total pay for the year based on the values will be £38110
How to calculate the amountSue's total pay of year will have three parts
Fixed Salary for 12 months
one month salary = £1410
so 12 month salary = £1410 x 12 = £16920
26% of total profit
Total cost to the company- £473,500
Total income for the company - £549,000
Profit = Total income for the company - Total cost to the company
= £549,000 - £473,500 = £75500
Sues income from profit = 26% of £75500 = (26 × 75500)/100 = £19630
Bonus if Sue sells at least 16 cars
Given number of months when sue solds atleast 16 cars = 4
So bonus income = 4 × 390 = £1560
Adding the three above parts
Sue's total pay for the year = £16920 + £19630 + £1560 = £38110
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Complete question
Ace autos sell cars and pay sue each month as follows
-salary of £1410
-26% of the total profit the company makes from her sales
- a £390 bonus if she sells at least 16 cars
The table shows information about the cars she sold last year
Total cost to the company- £473,500
Total income for the company - £549,000
Number of months when she sold at least 16 cars - 4
work out sues total pay for the year
here is my ? hrlp mr please
Based on the information, we can infer that the correct answer is 90° clockwise (option A).
How to identify the correct rotation?To identify the correct rotation of this figure we must perform the following procedure:
1. We must identify the reference figure.
2. We must identify the figure that expresses the rotation.
3. We must identify the angle of rotation of the figure.
4. Select the option that correctly expresses the sense of rotation.
Based on the above, we can infer that the correct answer is A. 90° Clockwise because the rotation is to the right.
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help with geometry please‼️‼️
Sam needs to fill a cylindrical container with punch. The container has
a radius of 11 inches and a height of 18 inches. How much punch can
Sam fit into the container?
Volume of the cylinder = 6838.92 cubic inches
We have to given that;
Sam needs to fill a cylindrical container with punch.
And, The container has a radius of 11 inches and a height of 18 inches.
Since, To determine the amount of cat litter the cylinder can hold, we need to calculate the volume of the cylinder.
Volume of a cylinder = πr²h
Where,
r=radius
h= height
Then,
π=22/7 or 3.14 (constant value)
r=11 inches
h=18 inches
Volume of a cylinder is,
= 3.14 × (11)² × 18
= 6838.92 cubic inches
Hence, Volume of the cylinder = 6838.92 cubic inches
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What is the volume of a square based pyramid with based side lengths of 6cm, a slant height of 7 cm, and a height of 5cm
Answer:
60 cm^3
Step-by-step explanation:
The formula for volume of a pyramid is
V = 1/3Bh, where B is the area of the base and h is the regular height (aka the altitude that connects the top of the pyramid and the base so we can simply ignore the slant height in the problem)
Step 1: The base of a square pyramid is a square and the formula for area (A) of a square is A = s^2, where s is the side.
Since we're told that the length of the base side length is 6 cm, we can find the area of the base:
A = 6^2 = 36
Step 2: Now, we can plug in 36 for B and 5 for h in the volume formula to find the volume:
V = 1/3(36)(5)
V = 12 * 5
V = 60 cm^3
What is the standard form of the equation of a quadratic function with roots of 2 and −5 that passes through (1, −3)?
y = −0.5x2 + 1.5x − 5
y = −0.5x2 + 1.5x + 5
y = 0.5x2 + 1.5x − 5
y = 0.5x2 + 1.5x + 5
The quadratic equation with the given roots is:
y = 0.5x² + 1.5x - 5
How to find the quadratic equation?For a quadratic equation with a leading coefficient a, and roots:
x = h and x = k, we will get general formula:
y = a*(x - h)*(x - k)
Here we know that the roots are x = 2 and x = -5, replacing that we will get:
y = a*(x - 2)*(x + 5)
And we know that this quadratic passes through (1, -3), replacing these values:
-3 = a*(1 - 2)*(1 + 5)
-3 = a*(-1)*(6)
-3 = -6a
-3/-6 = a
0.5 = a
Replacing that:
y = 0.5*(x - 2)*(x + 5)
Expanding the quadratic we will get:
y = 0.5x² + 1.5x - 5
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which of the decimals below are less than 0.7? select all that apply.
A) 0.65
B) 0.71
C) 0.54
D) 0.31
E) 0.84
estimate the original volume of the pyramid in fig 15.28 given that it's frustum has a 4 m by 4 m squared top which is 12 m vertically above the square base which is 20 m by 20 m (assume that the original problem was raised to a point . Neglect the volume of the entrance of the right of the photograph)
Answer:
Step-by-step explanation:
To estimate the original volume of the pyramid in Figure 15.28, we can use the formula for the volume of a frustum of a pyramid. The frustum is the portion of the pyramid between the top and bottom, created by removing the top section.
The formula for the volume of a frustum of a pyramid is:
V = (1/3) * h * (A + sqrt(A * B) + B)
Where:
V = Volume of the frustum
h = Height of the frustum (vertical distance between the top and bottom)
A = Area of the top base
B = Area of the bottom base
Given the dimensions provided, we can calculate the areas of the bases:
Area of the top base (A) = 4 m * 4 m = 16 m²
Area of the bottom base (B) = 20 m * 20 m = 400 m²
The height of the frustum (h) is given as 12 m.
Now we can plug these values into the formula:
V = (1/3) * 12 m * (16 m² + sqrt(16 m² * 400 m²) + 400 m²)
Calculating the square root and simplifying:
V = (1/3) * 12 m * (16 m² + 20 m² + 400 m²)
V = (1/3) * 12 m * (436 m²)
V = 1744 m³
Therefore, the estimated original volume of the pyramid in Figure 15.28 is approximately 1744 cubic meters.
The other day, I was taking care of two girls whose parents are mathematicians. The
girls are both whizzes at math. When I asked their ages, one girl replied,
our ages is 18.= The other stated, The difference of our ages is 4.= What is the
product of the girls’ ages?
Answer:
hey it is
Step-by-step explanation:
22 × 18 or 12 into 18
x+3x-4=2x+x+5
I don’t get this one need help
Answer:
x+3x-4=2x+x+5
Step-by-step explanation:
=4x-4= 3x+5
=4x-3x=5+4
= x=9. Done
2
Select the correct answer from the drop-down menu.
Which equation satisfies all three pairs of a and b values listed in the table?
a b
0-10
1 -7
2-4
The equation is
An equation that satisfies all three pairs of a and b values listed in the table include the following: C. 3a - b = 10.
How to determine an equation that satisfies all three pairs of a and b values listed in the table?In order to determine an equation that satisfies all three pairs of a and b values listed in the table, we would substitute each of the numerical values corresponding to each variable into the given equations and then evaluate as follows;
a - 3b = 10
0 - 3(-10) = 30 (False).
3a + b = 10
3(0) - 10 = -10 (False).
3a - b = 10
3(0) - (-10)
0 + 10 = 10 (True).
3a - b = 10
3(1) - (-7)
3 + 7 = 10 (True).
3a - b = 10
3(2) - (-4)
6 + 4 = 10 (True)
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Complete Question:
Which equation satisfies all three pairs of a and b values listed in the table?
a b
0 -10
1 -7
2 -4
The equation is?
A.) a-3b=10
B.) 3a+b=10
C.) 3a-b=10
D.) a+3b=10
On a standardized exam, the scores are normally distributed with a mean of 300 and a standard deviation of 40. Find the z-score of a person who scored 300 on the exam.
A z-score of 0 indicates that the person's score is equal to the mean, so they are right at the Average Performance level.the z-score of a person who scored 300 on the exam is 0.
The z-score of a person who scored 300 on the exam, we can use the formula:
z = (x - μ) / σ
where z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.
In this case, the person scored 300 on the exam, which is equal to the mean (μ). Therefore, we can substitute these values into the formula:
z = (300 - 300) / 40
Simplifying the equation, we have:
z = 0 / 40
Since any number divided by zero is undefined, we can conclude that the z-score of a person who scored 300 on the exam is 0.
The z-score measures the number of standard deviations a data point is away from the mean. In this case, a z-score of 0 indicates that the person's score is equal to the mean, so they are right at the average performance level.
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What formula would be used to find the future value? Return on balance 7.00% Monthly rate of return 0.583% Monthly payment -$200 Number of payments 120
Answer:
To calculate the future value (FV) of an investment with a given return on balance, monthly rate of return, monthly payment, and number of payments, you can use the future value of an ordinary annuity formula:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = Future value
P = Monthly payment
r = Monthly rate of return (expressed as a decimal)
n = Number of payments
In this case, the return on balance and the monthly rate of return are provided separately. To incorporate the return on balance into the monthly rate of return, you can use the following formula:
Effective Monthly Rate of Return = (1 + Monthly Rate of Return) * (1 + Return on Balance) - 1
Let's calculate the effective monthly rate of return using the given values:
Return on Balance = 7.00% (expressed as a decimal) = 0.07
Monthly Rate of Return = 0.583% (expressed as a decimal) = 0.00583
Effective Monthly Rate of Return = (1 + 0.00583) * (1 + 0.07) - 1
= 1.00583 * 1.07 - 1
= 1.0761281 - 1
= 0.0761281
Now that we have the effective monthly rate of return, we can use the future value formula to calculate the future value:
FV = -$200 * ((1 + 0.0761281)^120 - 1) / 0.0761281
Please note that since the monthly payment is negative (-$200), it indicates that it is an outgoing payment or an investment with regular withdrawals.
Calculating the above formula will give you the future value of the investment.
I hope I was helpful
The area A (r) (in square meters) of a circular algae colony with radius r meters is given by A (r)=ar².
13
The radius M (t) (in meters) after t minutes is given by M (t)=
Write a formula for the area Z (t) (in square meters) of the algae colony after t minutes.
The formula for the area Z (t) (in square meters) of the algae colony after t minutes: Z(t) = 13 * (1.02)² * t²
How to calculate the formulaThe area A(r) of a circular algae colony with radius r meters is given by
A(r) = pi * r²
The radius M(t) after t minutes is given by
M(t) = 1.02t
Substituting M(t) into the formula for A(r) gives
A(t) = pi * (1.02t)²
Simplifying gives
Z(t) = 13 * (1.02)² * t²
Therefore, the formula for the area Z (t) (in square meters) of the algae colony after t minutes: Z(t) = 13 * (1.02)² * t²
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please help me solve
Answer:
130 degrees
Step-by-step explanation:
DE+DA=130
What is the amount of discount
Answer: 26.40
Step-by-step explanation:
Which point would be a solution to the system of linear inequalities shown below?
The coordinates in the solution to the systems of inequalities is (12, 1)
Solving the systems of inequalitiesFrom the question, we have the following parameters that can be used in our computation:
y > -4x + 6
y > 1/3x - 7
Next, we plot the graph of the system of the inequalities
See attachment for the graph
From the graph, we have solution to the system to be the shaded region
The coordinates in the solution to the systems of inequalities graphically is (12, 1)
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Jackson bought 17 eggs from each farmer at the farmers’ market. Each farmer had an equal number of eggs.
Is this sample of eggs at the farmers market likely to be representative?
Without this information, it is not possible to determine if the sample accurately represents the overall distribution of eggs at the farmers' market.
It is impossible to say if the sample of eggs at the farmers' market is likely to be representative based on the information supplied. Jackson appears to have bought 17 eggs from each farmer, which suggests that he did so in an equal amount. It does not, however, provide data on the total number of farmers present at the market or their overall distribution of eggs.
Additional data, such as the total number of farmers present at the market, the average number of eggs each farmer generally has, and the variability in the number of eggs among the farmers, would be required to evaluate the sample's representativeness.
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9. Given that the figure below is a rhombus,
find the m<4.
The measure of the angle 4, m∠4, obtained from the measure formed by the diagonals of a rhombus is; m∠4 = 38°
What are the measures of the angles formed by the diagonals of a rhombus?The diagonals of a rhombus bisect the angles at the vertices of the rhombus
The diagonals of a rhombus are perpendicular bisectors of each other, therefore;
The measure of the angle m∠2 = 90°
Therefore; m∠1 = 90° - 52° = 38°
The triangle with base angles ∠1, and ∠4, is an isosceles triangle, with the base angles ∠1, and ∠4
The base angles of an isosceles triangle are congruent, therefore;
∠1 ≅ ∠4
m∠1 = m∠4
m∠4 = m∠1 = 38°
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100000+10000000000000=
Answer:
Step-by-step explanation:
The sum of 100,000 + 10,000,000,000,000 is 10,000,100,000,000.
Can someone please me with this question.
Correct form of the area of compound shape is:
Given,
Compound shape including triangle and rectangle.
Firstly , calculate the area of rectangle:
Area of rectangle = l* b
l= length of rectangle
b = breadth of rectangle
Thus,
Area of rectangle = 12*m
Secondly, area of triangle,
Area of triangle = 1/2 *b * h
b = base of triangle
h = height of triangle
Base of triangle = 12 - n
Then,
Area of triangle = 1/2* (12 - n) *m
Area of triangle = 6m - 0.5mn
Now to calculate the total area of the compound shape,
Total area = Area of rectangle + Area of triangle
Total area = 12m + (6m - 0.5mn)
Total area = 18m - 0.5mn
Hence option 3 satisfies the area of the compound shape .
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‼️WILL MARK BRAINLIEST, IF HELPFUL‼️
Answer:
A - The height of the parallelogram is equal to the radius of the circleB - The base of the parallelogram is equal to the circumference of the circle.C - The area of the circle is equal to the circumference times the radius.Step-by-step explanation:
Make a plan:
We can use the radius of the circle to calculate the height of the parallelogramWe can use the circumference of the circle to calculate the base of the parallelogramWe can use the parallelogram - like shape to show that the area of the circle is equal to the area of the parallelogram.Solve the problem:
A - The height of the parallelogram is equal to the circumference of the circleB - The base of the parallelogram is equal to the circumference of the circle.C - we can use the parallelogram-like shape to show that the area of the circle is equal to the area of the parallelogram. The area of the parallelogram is equal to the base times the height. However, the area of the circle is equal to the circumference times the radius.Draw the conclusion:
A - The height of the parallelogram is equal to the radius of the circleB - The base of the parallelogram is equal to the circumference of the circle.C - The area of the circle is equal to the circumference times the radius.Hope this helps!
the area of a trapizoid is 150 square millimeters 7mm 16mm 13mm what is the trapezoids height
The height of the trapezoid is approximately 13.043 mm.
Understanding How to Solve TrapezoidTo find the height of a trapezoid, you can use the formula:
Area = 1/2 * (base1 + base2) * height
Given:
Area = 150 square millimeters
base1 = 7 mm , w
base2 = 16 mm
150 = 1/2 * (7 + 16) * height
150 =1/2 * 23 * height
Make height the subject of the formula
300 = 23 * height
height = 300 / 23
height = 13.043 mm (rounded to three decimal places)
Therefore, the height of the trapezoid is approximately 13.043 mm.
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help me please with this question
Answer:A
Step-by-step explanation:
What is the equation for the given graph expressed in the form of y = a|x – h| + k?
The equation of the graph in the required form is y = 5|x| - 5
How to determine the equation for the graphFrom the question, we have the following parameters that can be used in our computation:
The graph (see attachment)
The graph is an absolute value graph
And it can be expressed in the form of y = a|x – h| + k
Where
Vertex = (h, k)
The vertex of the graph is (0, -5)
So, we have
y = a|x| - 5
Using the point on the graph, we have
a|1| - 5 = 0
So, we have
a = 5
This means that the equation of the graph is y = 5|x| - 5
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(50 points) Please help me i would really appreciate it
calculate the value of x and y
(multiple choice)
x = [select]
- 140
-120
-160
-100
y= [select]
-50
-60
-80
70
The values of the angles x and y are ∠x = 110 and ∠y = 70
How to calculate the values of x and yFrom the question, we have the following parameters that can be used in our computation:
The lines (parallel, transversal and others)
The measure of angle 1 is calculated as
∠1 = 180 - 140 -- angle on a straight line
So, we have
∠1 = 40
Next, we have
∠2 = 180 - 40 - 80 --- corresponding angles
So, we have
∠2 = 60
This means that
∠y = 180 - 60 - 50 -- angle on a straight line
So, we have
∠y = 70
This also means that
∠x = 180 - 60 - 10 -- angle in a triangle
So, we have
∠x = 110
Hence, the values of x and y are ∠x = 110 and ∠y = 70
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Use the number line to answer the question. A number line is shown with end points marked at the 2 and 2 tenths and 2 and 3 tenths. There are 9 tick marks between the two end points. Point H is on the third mark after 2 and 2 tenths. What is the decimal value of point H? Enter the answer in the box.
The decimal value of point H is then approximately 0.033333.
How to solve:
We must translate the position of the third mark after 2 and 2 tenths into a decimal value in order to determine the decimal value of point H.
We can determine the distance between each tick mark by dividing the distance between the two end points (2.3 - 2.2 = 0.1) by the total number of tick marks (9) because there are nine tick marks between the end points.
To get to point H, we can multiply the distance between each tick mark by the number of ticks: 0.1 / 9 = 0.011111.
The decimal value of point H is then approximately 0.033333.
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Which of these values for P and a will cause the function f(x)= Pa to be an
exponential growth function?
○ A. P= 1/2;a=1
OB. P = 2; a = 1
OC. P = 2; a = 3
O D. P = 1/2; a= 1/3
The values of P and a such that [tex]f(x) = Pa^x[/tex] is an exponential growth function are given as follows:
C. P = 2; a = 3.
How to define an exponential function?An exponential function has the definition presented according to the equation as follows:
[tex]y = ab^x[/tex]
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The conditions for an exponential growth function are given as follows:
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Assume that the graphs below shows a normal curve for a popular standardized test , the scores of which normally distributed .
All instruction are below, please show working
The probability that a randomly chosen person would score less than 86 is 0.8643, and the probability that a randomly chosen person would score more than 86 is 0.1357.
We consider X to be a random variable that represents the score of a person. So according to the question, X follows the given normal distribution and the given curve represents its distribution.
Now from the curve, we can see that the proportion of observation under the score 86 is 0.8643.
So we have,
P[X < 86] = 0.8643
A) We have to find the probability that a randomly chosen person would score less than 86. i.e, we have to find P[X < 86]
It is clearly given from the curve that, P[X < 86] = 0.8643
B) Now it is required to find the probability that a person chosen at random would score higher than 86 on this test. i.e P[X > 86]
P[X > 86] = 1 - P[X < 86]
= 0.1357
Therefore, the probability that a randomly chosen person would score less than 86 is 0.8643, and the probability that a randomly chosen person would score more than 86 is 0.1357.
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