A store sold 22 colored shirts and 8 white shirts.
Let x be the number of colored shorts and y be the number of white shirts.
A store sold 14 more colored shirts than white shirts.
so, we get an equation,
x = y + 14 ....................(1)
The white shirts cost $9.95, and the colored shirts cost $10.50. The store sold $310.60 worth of shirts.
So we get an equation,
10.50x + 9.95y = 310.60 .............(2)
Substitute above value of x in equation (2)
10.50(y + 14) + 9.95y = 310.60
10.50y + 147 + 9.95y = 310.60
20.45y = 310.60 - 147
20.45y = 163.6
y = 8
Substitute above value of y in equation (1)
So, x = 8 + 14
x = 22
Therefore, a store sold 22 colored shirts and 8 white shirts.
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Let f(x)=x^2−4 and g(x)=16−x. Perform the composition or operation indicated. (fg)(1)
Answer
The answer would be -45.
Step-by-step explanation:
I linked how I got this answer in the image. I hope this helps :)
Let f(x)=x − 3 and g(x)=x2−x. Find and simplify the expression. (f+g)(−6)
Answer: 33
Step-by-step explanation:
(f+g)(−6)=
f(-6)+g(-6)=
-6-3 + (-6)^2-(-6)=
-(6+3) + 36+6=
-9+42=
42-9=33
Which Macabacus add-in feature automatically calculates the column totals in the data table and inserts them into the column chart as displayed on the right?
Answer:
Yes
Step-by-step explanation:
Answer: Charts -> Stacked Totals -> Stacked Bar Totals
Step-by-step explanation:
after filling in in Macabacus the only add in feature that puts totals is stacked bar
Shantel told her hired hand Warren to gather eggs from the henhouse. Warren collected 30 eggs and brought them to Shantel. Shantel inspected
them and complained that 40% of them were broken. How many of them were still good eggs?
eggs were still good.
Answer:
18 eggs are still good.
Step-by-step explanation:
If 40% was broken then 60% are still good.
30(.6) = 18
Answer: 18 eggs were not broken and considered good.
Step-by-step explanation: 30 x 40% is the amount of eggs that were broken.
30 x 60% would be the amount of eggs that were still good.
This is becuase the total percentage must add up to be 100% between good eggs and broken eggs.
30 x .60 = 18 So 18 eggs were good
30 x .40 = 12, so that was the number of eggs that were broken
You could have done this problem two ways. Either calculate the broken eggs and subtract from the total. 30-12 = 18, or you could have just calculated the correct amount from figuring the percentage of eggs that were good from the beginning.
2+ I5rI = 12 Solve each equation
The solution of the equation for the values of r is -2 and 2.
What is referred as the modulus function?A modulus function returns the magnitude of such a number regardless of its sign. It's also known as the absolute value function.The modulus function, signified by |x| in mathematics, gives the modulus of a real number x. It returns a non-negative value for x. The modulus but rather absolute value of the a number is also known as the number's distance from its origin or zero.For the expression
2+ I5rI = 12
Subtract both side by 2
2 + I5rI -2 = 12 - 2
I5rI = 10
Open the modulus function as;
-5r = 10+5r = 10Solve for each term
-5r = 10
Divide both side by -5,
r = 2
Now,
5r = 10
Divide both side by 5,
r = 2
Therefore, the solution of the equation is for r = -2 and 2.
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Find the area, in square units, of AABC plotted below.
C(-6,-2)
D(-7,-5) d
A(-4,-6)
B(2,-8)
Check the picture below.
so the base of that triangle is AB whilst the height of it is CD, so let's get them
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-6})\qquad B(\stackrel{x_2}{2}~,~\stackrel{y_2}{-8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AB=\sqrt{(~~2 - (-4)~~)^2 + (~~-8 - (-6)~~)^2} \implies AB=\sqrt{(2 +4)^2 + (-8 +6)^2} \\\\\\ AB=\sqrt{( 6 )^2 + ( -2 )^2} \implies AB=\sqrt{ 36 + 4 } \implies AB=\sqrt{ 40 }\implies \stackrel{base}{AB=2\sqrt{10}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ C(\stackrel{x_1}{-6}~,~\stackrel{y_1}{-2})\qquad D(\stackrel{x_2}{-7}~,~\stackrel{y_2}{-5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ CD=\sqrt{(~~-7 - (-6)~~)^2 + (~~-5 - (-2)~~)^2} \\\\\\ CD=\sqrt{(-7 +6)^2 + (-5 +2)^2} \\\\\\ CD=\sqrt{( -1 )^2 + ( -3 )^2} \implies CD=\sqrt{ 1 + 9 } \implies \stackrel{height}{CD=\sqrt{ 10 }} \\\\[-0.35em] ~\dotfill[/tex]
[tex]A=\cfrac{1}{2}(\stackrel{b}{2\sqrt{10}})(\stackrel{h}{\sqrt{10}})\implies A=\sqrt{10}\cdot \sqrt{10}\implies A=\sqrt{10^2}\implies {\Large \begin{array}{llll} A=10 \end{array}}[/tex]
A plant biologist studies the height of sunflowers. He measures a large sample of sunflowers and creates a probability distribution. The distribution is normal in shape with mean 112 cm and standard deviation 16 cm.
What is the probability (approximately) that a sunflower will be less than 136 cm tall?
Enter a number in decimal form, e.g. 0.68, not 68 or 68%.
The probability that sunflower will be less than 136 cm tall is 0.9332.
How to calculate the probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
From the information, the biologist measures a large sample of sunflowers and creates a probability distribution and the distribution is normal in shape with a mean 112 cm and a standard deviation 16 cm.
It should be noted that the following can be deduced:
Mean = 112
Standard deviation = 16
Sunflower should be less than 136. This will be x < 136.
Therefore, the probability will be;
P(X < 136)
= P(Z < [(number - mean) / standard deviation)]
= P(Z < [136 - 112)/16]
= P(Z < 1.50)
= 0.9332
It should be noted that the probability is gotten by looking at the value of x in the z table.
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1) Is it possible to end up with two different prime factorizations for a number, or will you always end up with the same list of prime factors?
2) What was true about all of the numbers in the final lists of factors? Why?
3) Can two different numbers have the same prime factorization? Why or why not?
4) Explain how writing a number as a product of prime numbers is a way of representing that number.
How does knowing that the prime factorization of 40 is 2 × 2 × 2 × 5 help you know every possible factor of 40?
5) How is what you did in the Action Task related to the colour code in the Minds On Activity?
1) A prime factorization of a particular number will always give the same prime factors.
2) All the factors in the list when multiplied will give the original number.
3) No, two different numbers cannot have the same prime factorization.
4) The prime factors of 40 are 2 and 5.
1) We anticipate finding factors in prime factorization that can add to themselves to get the original number. The original number can be obtained by multiplying the remaining components together as long as the first factor can divide the quantity without leaving a remnant.
Prime factorization of the number, 15 goes thus;
15/3=5
5/5=1
3*5=15
So, all the factors multiply to give the original number.
2) Numbers that split an original number evenly or precisely are known as its factors. A factor is a whole number that can divide a larger number in two equal halves.
3) The collection of prime numbers that can be multiplied together to produce a given number is known as the prime factorization of that number. Because the same set of numbers must provide the same result when multiplied together, two separate numbers cannot have the same prime factorization.
4) Any number can be represented as a sum of prime numbers using prime factorization. A number with exactly two elements, 1 and the number itself, is said to be a prime number. As an illustration, the prime factorization of 18 is 2 3 3. Here, the two main elements or prime factors of 18 are 2 and 3.
The prime factorization of 40 is :
40 = 2 × 2 × 2 × 5
Hence, the prime factors of 40 are 4 and 5.
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Population of Arkansas is currently 3 million people. If it grew by just 5%, what would the new population be?
Please mark me brainliest. please
Population of Arkansas is currently 3 million people. If it grew by just 5%, what would the new population be?
Answer : 3,150,000 people
Step-by-step explanation:
3,000,000 + 5% = 3,150,000
what is the domain of the relation shown below?
Help 4567778776655555
In order to calculate the function (f/g)(x), we need to divide f(x) by g(x).
First, let's find the zeros of the function f(x), so we can write it in the factored form:
[tex]\begin{gathered} f(x)=-10x^2+30x+40\\ \\ a=-10,b=30,c=40\\ \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\ \\ x=\frac{-30\pm\sqrt{900+1600}}{-20}\\ \\ x_1=\frac{-30+50}{-20}=-1\\ \\ x_2=\frac{-30-50}{-20}=4 \end{gathered}[/tex]So the factored form is:
[tex]\begin{gathered} f(x)=a(x-x_1)(x-x_2)\\ \\ f(x)=-10(x+1)(x-4) \end{gathered}[/tex]Now, calculating the composite function, we have:
[tex]\frac{f(x)}{g(x)}=\frac{-10(x+1)(x-4)}{-5x-5}=\frac{-10(x+1)(x-4)}{-5(x+1)}=2(x-4)=2x-8[/tex]A scale diagram of a bridge is shown below where 1cm repsents 7cm canculate the length of the brigde in real life give your answer in meters
Using the scale factor we calculate the length of the bridge to be 5.6 meters.
Scaling is a linear transformation that raises or decreases the size of objects by a constant scale factor in all directions.
The result of uniform scaling is geometrically equivalent to the original. In common usage, a scale factor of 1 is allowed, allowing congruent shapes to be categorized as comparable.A map's scale is typically defined as the distance between one unit on the map and the corresponding distance on the ground. This ratio is known as a scale factor.Scale factor equals the new shape's dimensions.The length of the bridge on the map is 80 cm .
Now the scale of the map is 1 : 7
Therefore the length of the bridge is 80 × 7 = 560 cm = 5.6 meters.
Hence the length of the bridge is 5.6 meters.
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Joanne and her friends went on a hiking vacation to the national park. They
covered 2 miles on the first day. They went on a 4-mile hike and 8-mile hike on
day 2 and day 3, and the hiking distance continued to increase in a geometric
sequence. How many miles did Joanne and her friends hike on the 4th day?
Answer: 16 miles
Step-by-step explanation:.
Can someone help with this question?✨
The equation of the line parallel to y = 4x - 2 and passes through (1, 8) is
y = 4x + 4
How to find equation for a line?The equation of a line can be represented as follows:
y = mx + b
where
m = slope of the linesb = y-interceptTherefore, the equation of a line is parallel to y = 4x - 2 and passes through (1, 8)
Parallel lines have the same slope.
Therefore,
y = 4x + b
let's find y-intercept using (1, 8)
8 = 4(1) + b
b = 8 - 4
b = 4
Therefore,
the equation of the line is y = 4x + 4
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Find the P-value for a test to support the claim that less than 50% of the people following a particular diet will experience increased energy. Of 100 randomly selected subjects who followed the diet, 47 noticed an increase in their energy level.
The P-value for a test to support the claim that less than 50% of the people is 0.2743.
What is p value?The p-value is a figure that, when generated from a statistical test, indicates how likely it is that, if the null hypothesis were true, you would have discovered a certain collection of observations.
This will be illustrated thus:
Sample proportion = 47 / 100 = 0.47
Test statistics = {p} - p) / ✓ [ p( 1 - p) / n )
= ( 0.47 - 0.50) / ✓ 0.50 * 0.50 / 100)
= -0.6
p-value = P(Z < z)
= P(Z < -0.6)
This will be looked at on the distribution table. The value will be 0.2743.
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grade 12 mathematics
The value is =[tex]\frac{-73}{22}[/tex]
What is limit ?The values that a function approaches for the specified input values are known as limits in mathematics. Limits are essential to calculus and mathematical analysis because they help define concepts like integrals, derivatives, and continuity. It's employed in the analysis process and always has to do with how the function behaves at a specific moment. In the idea of the limit of a topological net, the limit of a sequence is further generalized and connected to the limit and direct limit in the theory category.
Given That : [tex]\lim_{x \to \33} \frac{(Fx)^{3}-3x }{2x^{2} -f(x)}[/tex] and f(x)= -4
[tex]\lim_{x \to \33} \frac{(Fx)^{3}-3x }{2x^{2} -f(x)}[/tex]
F(x)= -4
=[tex]\frac{-64-9}{18+4}[/tex]
=[tex]\frac{-73}{22}[/tex]
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Part I
Find the domain and the range of the following function.
f(x)=
x+3, for x≤ -3
1, for -3
1/2x, for x ≥4
The domain of the function is
(Type your answer in interval notation)
Range and Domain. The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
What Separates a Function's Domain from its Range?
A function's domain and range are its constituent parts. In contrast to a function's range, which is the set of all potential outputs, a function's domain is the set of all possible inputs.
All real numbers fall under the expression's domain, with the exception of cases where it is undefined. No real number exists in this situation, rendering the statement undefinable.
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A monument is made in the form of a right pyramid with a regular hexagon as a base. each base side is 5 meters and the slant height is 30 meters. if only the sides (and not the base) of the monument is to be covered by metal, how many square meters of metal are needed to cover the sides of the pyramid?
A. 450 m 2
B. 300 m 2
C. 75 m 2
D. 150 m 2
450 m² of metal are needed to cover the sides of the pyramid.
The correct answer is an option (A)
In this question, a monument is made in the form of a right pyramid with a regular hexagon as a base. each base side is 5 meters and the slant height is 30 meters.
If only the sides (and not the base) of the monument is to be covered by metal, we need to find the amount of metal needed to cover the sides of the pyramid.
Since the base of the pyramid is hexagon, there are 6 triangular sides of the pyramid.
We need to find the area of 6 triangular surfaces.
The base of the triangle b = 5 meters and the height of the triangle is the slant height of the pyramid.
h = 30 meters
So, area of the one triangular surface would be,
A1 = 1/2 × b × h
A1 = 1/2 × 5 × 30
A1 = 5 × 15
A1 = 75 square meters
And the area of the 6 triangular surfaces would be,
A = 6 × A1
A = 6 × 75
A = 450 square meters
Therefore, 450 m² of metal are needed to cover the sides of the pyramid.
The correct answer is an option (A)
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area of composite figures worksheet #1 (don’t mind the pen it’s a mistake)
Answer:
Given that,
Rectangular room is of the dimension 12 feet by 18 feet
To find the number of square feet of carpet needed.
Explanation:
Area of the rectangle is,
[tex]\text{ length}\times\text{ breadth}[/tex]Area of the rectangular room is,
[tex]12\times18[/tex][tex]=270\text{ ft}^2[/tex]Area of the rectangular room is 270 square feet.
Therefore, 270 square feet of carpet are needed to cover the room.
we know that,
[tex]1\text{ yard }=3\text{ feet}[/tex]Using this conversion we get,
[tex]270\text{ ft}^2=270(\frac{1}{3}\text{ yd})^2[/tex]If a skier travels 4700 feet up a ski lift whose angle of inclination is 30°, how high above his starting level is the skier?
If a skier travels 4700 feet up a ski lift whose angle of inclination is 30°, how high above his starting level is the skier is 2350 feet.
HeightGiven data:
Distance = 4700 feet
Angle of inclination = 30°
Now let determine the height by formulating an equation which will help us to find the height
4700 × sin 30°
Where:
Sin 30° = 0.5 or 1/2
Hence,
Height :
Height = 4700 feet × 0.5
Height = 2350 feet
So,
Height = 2350 feet above the starting level
Therefore we can conclude that the skier is 2350 feet above the starting level.
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Solve the equation.
−3=z−8
Answer:
add -8 to -3 so thats 5 and your answer is 5=z
Step-by-step explanation:
9(x)=1/4x+1
What is g(-16)?
G(-16)=
Answer:
1; 4/35
2; -16g
sorry if wrong
What is an equation of the line that passes through the points (5, 0) and
-2, -3)?
Answer:
Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.
Find gradient of the line first.
Formula of gradient is given as y2-y1 ÷ x2-x1 or y1-y2 ÷ x1-x2, where x and y are the coordinates of the points.
Gradient = (-3-0) ÷ (-2-5) = 3/7
Eqn is y = 3/7x + c
Substitute either one of the coordinates into the equation to find c.
0 = 3/7(5) + c
c = -15/7
Hence, the equation of the line is y = 3/7x - 15/7
A merchant bought several pieces of silk for $70. He sold all but two of them at a profit of $4 per piece. His total profit was $18. How many pieces did he originally purchase?
A merchant bought several pieces of silk for $70. He sold all but two of them at a profit of $4 per piece. His total profit was $18. How many pieces did he originally purchase?
Let n be the number of pieces. He sold n - 2 pieces
Let p be the original price. His selling price = p + 4
Then n · p = 70.00
And (n - 2) · (p + 4) = 70.00+18.00 ---> np + 4n - 2p - 8 = 88.00
---> np + 4n - 2p = 96.00
---> 70.00 + 4n - 2p = 96.00
4n - 2p = 26.00
2n - p = 13.00
Trying some possibilities (7 & 1), (8 & 3), (9 & 5), and (10 & 7), finally gets us to the answer: n = 10 and p = 7.00.
therefore
the number of pieces was 104 1/3 — 2 7/9
Please help quick
Answer: 1 2/3 or 5/3
Step-by-step explanation: if you change 4 1/3 to a different denominator of 9, you will get 4 3/9. Then, you will do 4 3/9-2 7/9 which equals 1 2/3.
What is 2M?
M=[3 5
-4 0]
The value of matrix 2M is [tex]\left[\begin{array}{ccc}6&10\\-8&0\\\end{array}\right][/tex]
What is matrix ?A matrix is a collection of numbers that have been put in rows and columns to make a rectangular array. The entries of the matrix are the numbers, which are referred to as its elements. In addition to many areas of mathematics, matrices are widely used in the fields of engineering, physics, economics, and statistics. The representation of rotations and other picture changes has been accomplished using matrices, which have significant uses in computer graphics.
How to do Matrix Multiplication ?Multiplication of matrices, often known as matrix multiplication, is one of the operations that can be carried out on matrices in linear algebra. If the two matrices given, A and B, are compatible, then matrix A and matrix B can be multiplied. The binary operation of multiplying matrices produces a matrix from two input matrices.
M = [tex]\left[\begin{array}{ccc}3&5\\-4&0\\\end{array}\right][/tex]
2M = 2 [tex]\left[\begin{array}{ccc}3&5\\-4&0\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}6&10\\-8&0\\\end{array}\right][/tex]
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what is the slope of 10x + 5y = 30
Answer:
[tex]y=-2x+6[/tex]
So, the slope is -2.
Step-by-step explanation:
Solve the literal equation for y and use the slope value formed.
[tex]10x+5y=30\\5y=-10x+30\\\frac{5y}{5}=\frac{-10}{5}x+\frac{30}{5}\\y=-2x+6[/tex]
So, according to [tex]y=mx+b[/tex], the slope is -2 where m is the slope.
Answer:
i swear your going to give a head ack i told you the answer
Step-by-step explanation:
Please help I’ll mark you as brainliest if correct!!!
Answer:
1710
Step-by-step explanation:
simplify | 1×10^3 + 7×10^2 + 4×10 = 1710
A cell phone company charges $55 a month for unlimited text and $0.50 per minute for phone calls. The bill last month was $66. Write an equation to find out how many minutes for phone calls were charged on the bill. (use notes in the Schoology "Notes" folder)
we can write an equation
[tex]T=55+0.50m[/tex]where T is the total price, 55 the fixed charge, 0.5 the cost per minute and m the minutes used
if the total is 66 we must to replace T=66 and solve m
so
[tex]\begin{gathered} 66=55+0.50m \\ 0.50m=66-55 \\ m=\frac{11}{0.50} \\ \\ m=22 \end{gathered}[/tex]were charged 22 minutes on the bill
Two similar solids are given, find the missing information. Please
step 1
Find out the scale factor
Remember that
If two figures are similar, then the ratio of their volumes is equal to the scale factor elevated to the cubic
so
Let
s ----> scale factor
s^3=11,000/8,019
s=1.11
step 2
Remember that
If two figures are similar, then the ratio of their surface areas is equal to the scale factor squared
so
s^2=SA/1,134
s=1.11
1.11^2=SA/1,134
SA=(1.11)^2*(1,134)
SA=1,400 yd2
The answer is 1,400 square yards