The store wants to make a 20% profit:
Multiply the cost of the toy by 1.20 ( cost plus 20%).
6.25 x 1.20 = $7.50
This means when the toy is sold at 25% off, it needs to be $7.50 to make the 20% profit.
When the item is 25% off, that means it would sell for 75% of the original price.
Now to find what the price needs to be before the 25% off divide the profit price by 75%
7.50 / 0.75 = $10
K = $10
Final answer:
To find the price at which the toy should be sold to maintain a 20% profit after a 25% discount, use the cost price and profit margin to calculate the selling price.
Explanation:
To compute the price at which the toy should be priced at a 25% discount and still make a profit of 20%, follow these steps:
Calculate the cost price after a 20% profit margin: $6.25 + 0.20 * $6.25 = $7.50
Set up the equation: $7.50 = (100% - 25%) * $k
Solve for k: $k = $7.50 / 0.75 = $10
Solve F(x) for given domain. Include all of your work in your final work submit your solution
F(x)=x^2+2
F(x^2)=
PLEASE HELP I'AM SCREAMING FOR HELP!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
Actually, you have not "given" the domain.
The domain of F(x)=x^2+2 is "the set of all real numbers," because F(x)=x^2+2 is a polynomial.
F(x^2) = (x^2) + 2 = x^4 + 2. Again, this is a polynomial and the domain is "the set of all real numbers."
Double check to ensure that you have copied down this problem correctly.
The temperature was t degrees farenheight . It fell 8 degrees farenheight and is now 32 degrees farenheight.What was the orginal temperature?
The fraction four-fifths is equivalent to what percent?
The answer is:
The fraction is equivalent to 80%.
Why?To solve the problem, we need to remember that if we want to convert from numbers to percentual values, we need to multiply the given number by 100.
So, if we have the fraction four-fifths which is:
[tex]\frac{4}{5}=0.8[/tex]
If we need to convert it to percent, we need to multiply it by 100:
[tex]0.8*100=80(percent)[/tex]
Hence, we have that the fraction is equivalent to 80%.
Have a nice day!
Answer:
80%
Step-by-step explanation:
We know 4/5 is the same as 4 divided by 5 then using long division for 4 divided by 5 gives us 0.8 converting our number to a percent
0.8 x 100 = 80%
Sketch the graph of y= (x - 2)2 - 16, then select the graph that corresponds
to your sketch.
-20
O A. Graph A
O B. Graph B
O C. Graph c
O D. Graph D
If there was an illustration, I would be happy to assist you.
A gardener is planting two types of trees:Type A is three feet tall and grows at a rate of 15 inches per year.Type Bis four feet tall and grows at a rate of 10 inches per years. Determine exactly How long many years it will take for these trees to be the same height
Answer:
2.4 years
Step-by-step explanation:
you have to first convert the trees' heights into inches. three feet is equivalent to 36 inches and four feet is equivalent to 48 inches. Since three A grows at 15 inches a year it'll become a the expression 15x+36 and the expression for tree B will be 10x+48. You set them up to each other and simplify it.
15x+36=10x+48
-10x -10x
5x+36=48
-36 -36
5x=12
/5 /5
x=2.4
So it'll be 2.4 years
sollve for x (x-5)=4x-5
Answer:
x=0
Step-by-step explanation:
(x-5)=4x-5
Subtract x from each side
x-5-x=4x-x-5
-5 = 3x-5
Add 5 to each side
-5+5 = 3x-5+5
0 = 3x
Divide by 3
0/3 = 3x/3
0 =x
x=0
Which statements are true for the functions g(x) = x^2 and h(x) = –x^2 ? Check all that apply.A.For any value of x, g(x) will always be greater than h(x).B.For any value of x, h(x) will always be greater than g(x).C.g(x) > h(x) for x = -1. D.g(x) < h(x) for x = 3. E.For positive values of x, g(x) > h(x). F.For negative values of x, g(x) > h(x)
Answer:
C, E, F
Step-by-step explanation:
The range of the function [tex]g(x)=x^2[/tex] is [tex]y\in [0,\infty)[/tex], the range of the function [tex]h(x)=-x^2[/tex] is [tex](-\infty,0][/tex]
This means that for any value of x, the value of [tex]g(x)[/tex] is always greater or equal to the value of [tex]h(x)[/tex] (the values are equal at x=0).
So, options A and B are false, because at x=0 the values are equal and h(x) cannot be greater than g(x)
Options C, E and F are true, because for all non-zero x, g(x)>h(x).
Option D is false (the reason is the same as for option B)
The table represents a linear equation. Which equation correctly uses point (–2, –6) to write the equation of this line in point-slope form? y – 6 = (x – 2) y – 6 = (x – 2) y + 6 = (x + 2) y + 6 = (x + 2)
Answer:
[tex]y+6=m(x+2)[/tex]
where I would have to look at the table to know [tex]m[/tex].
Step-by-step explanation:
Point-slope form of a line is
[tex]y-y_1=m(x-x_1)[/tex]
where [tex]m \text{ is the slope and } (x_1,y_1) \text{ is a point on that line}[/tex]
You are given [tex](x_1,y_1)=(-2,-6) \text{, but no value for }m[/tex].
So we know we are looking for an equation that looks like this:
[tex]y-(-6)=m(x-(-2))[/tex]
If you simplify this looks like:
[tex]y+6=m(x+2)[/tex]
Answer:
d
Step-by-step explanation:
Select all that apply.
Which numbers are not perfect squares?
25
20
18
36
16
14
24
Answer:
14, 18, 20, and 24 are not perfect squares.
The numbers that are not perfect squares are:
1. 20
2. 18
3. 14
4. 24
These numbers do not have integer square roots, which means they are not perfect squares.
A perfect square is a number that can be expressed as the product of an integer multiplied by itself. For example, 25 is a perfect square because [tex]\(5 \times 5 = 25\).[/tex]
Let's examine each number:
1. 25 - This is a perfect square because [tex]\(5 \times 5 = 25\).[/tex]
2. 20 - This is not a perfect square. It cannot be expressed as the product of an integer multiplied by itself.
3. 18 - This is not a perfect square. It cannot be expressed as the product of an integer multiplied by itself.
4. 36 - This is a perfect square because [tex]\(6 \times 6 = 36\).[/tex]
5. 16 - This is a perfect square because [tex]\(4 \times 4 = 16\).[/tex]
6. 14 - This is not a perfect square. It cannot be expressed as the product of an integer multiplied by itself.
7. 24 - This is not a perfect square. It cannot be expressed as the product of an integer multiplied by itself.
Therefore, the numbers that are not perfect squares are 20, 18, 14, and 24. They cannot be represented as the square of an integer. The other numbers, 25, 36, and 16, are perfect squares as they can be expressed as the square of an integer.
The complete question is here.
Which numbers are not perfect squares? 25 20 18 36 16 14 24
In triangle ΔABC, ∠C is a right angle and segment CD is the height to segment AB . Find the angles in ΔCBD and ΔCAD if m∠A = 20°
m∠CDB =
m∠CBD =
m∠BCD =
m∠CDA =
m∠ CAD=
m∠ACD =
Step-by-step explanation:
Draw a picture (like the image below).
Notice that triangles ABC and ACD both contain right angles, and both contain angle A (20°). Since angles of a triangle add up to 180°, that means their third angle must also be the same (70°).
Also notice that triangles ABC and CBD both contain right angles, and both contain angle B (70°). So their third angle must also be the same (20°).
Therefore:
m∠CDB = 90°
m∠CBD = 70°
m∠BCD = 20°
m∠CDA = 90°
m∠CAD = 20°
m∠ACD = 70°
[tex]( \sqrt{5x + 6} ) ^{2} [/tex]
multiply
[tex]\bf (\sqrt{5x+6})^2\implies \sqrt{(5x+6)^2}\implies 5x+6[/tex]
Which is an exponential decay function?
Step-by-step explanation:
exponential decay functions are written in the form :
[tex]y=ab^{x}[/tex]
where b is less than 1
if we look at the 3rd choice and consider the term on the right.
[tex](8/7)^{-x}[/tex]
= [tex](7/8)^{x}[/tex]
If we compare this to the general form above,
b = 7/8 (which is less than 1)
hence the 3rd choice is correct.
The function which is an exponential decay function is:
[tex]f(x)=\dfrac{3}{2}(\dfrac{8}{7})^{-x}[/tex]
Step-by-step explanation:We know that an exponential function is in the form of:
[tex]f(x)=ab^x[/tex]
where a>0 and if 0<b<1 then the function is a exponential decay function.
and if b>1 then the function is a exponential growth function.
a)
[tex]f(x)=\dfrac{3}{4}(\dfrac{7}{4})^x[/tex]
Here
[tex]b=\dfrac{7}{4}>1[/tex]
Hence, the function is a exponential growth function.
b)
[tex]f(x)=\dfrac{2}{3}(\dfrac{4}{5})^{-x}[/tex]
We know that:
[tex]a^{-x}=(\dfrac{1}{a})^x[/tex]
Hence, we have the function f(x) as:
[tex]f(x)=\dfrac{2}{3}(\dfrac{5}{4})^x[/tex]
Here
[tex]b=\dfrac{5}{4}>1[/tex]
Hence, the function is a exponential growth function.
c)
[tex]f(x)=\dfrac{3}{2}(\dfrac{8}{7})^{-x}[/tex]
We know that:
[tex]a^{-x}=(\dfrac{1}{a})^x[/tex]
Hence, we have the function f(x) as:
[tex]f(x)=\dfrac{3}{2}(\dfrac{7}{8})^x[/tex]
Here
[tex]b=\dfrac{7}{8}<1[/tex]
Hence, the function is a exponential decay function.
d)
[tex]f(x)=\dfrac{1}{3}(\dfrac{9}{2})^x[/tex]
Here
[tex]b=\dfrac{9}{2}>1[/tex]
Hence, the function is a exponential growth function.
What is the solution of this equation
4x-6=10x-3
Answer:
x=[tex]\frac{-1}{2}[/tex]
Step-by-step explanation:
4x-6=10x-3 (add 6 to both sides)
4x=10x+3 (subtract 10x from both sides)
-6x=3 (divide both sides by -6)
x=[tex]\frac{-1}{2}[/tex]
Answer: X = -1/2
Step-by-step explanation: Your goal is to isolate x. First, subtract 4x from each side.
-6 = 6x - 3
Add 3 on both sides.
-3 = 6x
Divide by 6 on each side.
X = -1/2
Factor completely 2x3 + x2 − 18x − 9.
(x2 − 9)(2x + 1)
(x − 3)(x + 3)(2x − 1)
(x − 3)(x + 3)(2x + 1)
(2x − 3)(2x + 3)(x − 1)
Answer:
Option C: (x − 3)(x + 3)(2x + 1)
Step-by-step explanation:
Only a few minutes please help!!
A) 20
B) 50
C) 90
D) 120
Answer:
C 90
Step-by-step explanation:
Answer: OPTION B.
Step-by-step explanation:
You can observe in the figure provided that the angle 3 and the angle that measures 70° , share the same vertex, therefore, you can conclude that they are Vertical angles and they are congruent. Then:
[tex]m\angle 3=70\°[/tex]
You can notice that the angle 1 and the angle that measures 70° are Complementary angles (They add up to 90°), then you can find the measure of the angle 1:
[tex]m\angle 1+70\°=90\°\\\\m\angle 1=90\°-70\°\\\\m\angle 1=20\°[/tex]
Then:
[tex]m\angle 3-m\angle 1=70\°-20\°\\\\m\angle 3-m\angle 1=50\°[/tex]
use the substitution method to solve the system of equations choose the correct orderd pair. 3x-y=7 2x-2y=2
Answer:
(3,2)
Step-by-step explanation:
We are given the system:
3x-y=7
2x-2y=2.
We are asked to solve this by substitution. We need to pick an equation and pick a variable from that equation to solve for that variable.
I really like either for this. Some people might go with the first one though. Let's do that. I will solve the first one for y.
3x-y=7
Subtract 3x on both sides:
-y=-3x+7
Divide both sides by -1:
y=3x-7
Now we are ready for substitution. We are going to plug this equation into the second equation giving us:
2x-2y=2 with y=3x-7 gives us:
2x-2(3x-7)=2
Distribute:
2x-6x+14=2
Combine like terms:
-4x+14=2
Subtract 14 on both sides:
-4x =2-14
Simplify:
-4x =-12
Divide both sides by -4:
x =-12/-4
Simplify:
x =3
So using y=3x-7 and x=3, I will find y now.
y=3x-7 if x=3
y=3(3)-7 (I inserted 3 for x since we had x=3)
y=9-7 (Simplified)
y=2 (Simplified)
The answer is (x,y)=(3,2).
Ivan's gas tank is 1/5 full. After he buys 7 gallons of gas, it is 7/10 full. How many gallons can Ivan's tank hold?
Answer: 14 gallons of gas.
Step-by-step explanation: For the fractions, find a common denominator, which would be 10. To get 1/5 to have a denominator of 10, multiply each number by 2. You would get 2/10. 7 gallons fills his tank from 2/10 to 7/10. Subtract the two fractions.
7/10 - 2/10 = 5/10.
7 gallons filled his tank half way. We are trying to find the amount to fill his tank all the way. So multiply 7 by 2.
7 x 2 = 14
14 gallons of gas will fill his tank all the way.
I hope this helps!
Ivan's gas tank can hold 17.5 gallons when full after being 1/5 full and then adding 7 gallons.
The total capacity of Ivan's gas tank:
From 1/5 to 7/10 full means it increased by 4/10 or 2/5 of its capacity.Since 7 gallons represent 2/5, to find the total capacity, we divide 7 by 2/5 or multiply by 5/2.Therefore, the total capacity of Ivan's gas tank is 17.5 gallons.help me to do this question friends
Answer:
(1, 1 )
Step-by-step explanation:
Given the 2 equations
2x + 3y = 5 → (1)
3x + 2y = 5 → (2)
We can eliminate the term in x by multiplying (1) by 3 and (2) by - 2
6x + 9y = 15 → (3)
- 6x - 4y = - 10 → (4)
Add (3) and (4) term by term
(6x - 6x) + (9y - 4y) = (15 - 10), that is
5y = 5 ( divide both sides by 5 )
y = 1
Substitute y = 1 in either (1) or (2) and solve for x
Substituting in (1), then
2x + (3 × 1) = 5
2x + 3 = 5 ( subtract 3 from both sides )
2x = 2 ( divide both sides by 2 )
x = 1
Solution is (1, 1 )
Which expression represents the prime factorization of 96?
A. 2 x 2 x 3 x 8
B. 2 x 2 x 2 x 12
C. 2 x 2 x 2 x 2 x 2 x 3
D. 2 x 2 x 2 x 2 x 2 x 3 x 3
It is not A. because 8 is not a prime number.
It is not B. because 12 is not a prime number.
C. 2 x 2 x 2 x 2 x 2 x 3 = 4*4*6= 96
D. 2 x 2 x 2 x 2 x 2 x 3 x 3= 4*4*6*3=16*18= 288
Answer is C. -2 x 2 x 2 x 2 x 2 x 3 : 96 ( not D. = 298 , 298 is greater than 96)
The prime factorization of the number 96 is 2 x 2 x 2 x 2 x 2 x 3. The correct option is C.
What is prime factorization?A number can be expressed as a product of its prime factors through the process of prime factorization. Prime factorization is the process of factorizing the bigger numbers in a way that all the numbers are prime.
Any natural number higher than 1 that is not the sum of two smaller natural numbers is referred to be a prime number. A composite number is any natural number greater than one that is not prime.
The given number is 96. The factorization of the number 96 will be done as below:-
96 = 2 x 2 x 2 x 2 x 2 x 3
Therefore, the prime factorization of the number 96 is 2 x 2 x 2 x 2 x 2 x 3. The correct option is C.
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Which of the following reveals the minimum value for the equation 2x^2 + 12x − 14 = 0?
The equation that reveals the minimum value for the equation is 2(x + 3)² = 32
Which reveals the minimum value for the equation
From the question, we have the following parameters that can be used in our computation:
2x² + 12x − 14 = 0
Rewrite as
2x² + 12x = 14
So, we have
2(x² + 6x) = 14
Take the coefficient of x
k = 6
Divide by 2
k/2 = 3
Square both sides
(k/2)² = 9
So, we have
2(x² + 6x + 9) = 14 + 2 * 9
2(x² + 6x + 9) = 32
Express as squares
2(x + 3)² = 32
Hence, the equation that reveals the minimum value for the equation is 2(x + 3)² = 32
Question
Which of the following reveals the minimum value for the equation 2x^2 + 12x - 14 = 0?
2(x + 6)^2 = 26
2(x + 6)^2 = 20
2(x + 3)^2 = 32
The surface area of the prism is ______ square units. All measurements in the image below are in units. (Input whole number only.) A triangular prism is shown with 2 right triangular sides having legs 3 and 4 and hypotenuse 5. The length of the prism is 3.5 Numerical Answers Expected! Answer for Blank 1:
Answer:
54
Step-by-step explanation:
Answer:
54 square units
Step-by-step explanation:
In order to calculate the surface area of the prism you have to calculate the area of each face of the prism, and you have to remember the different formulas to calculate the areas:
[tex]Rectangle=Length*Width[/tex]
[tex]Triangle=\frac{Base*Height}{2}[/tex]
So you just have to insert the values into the formulas:
[tex]Rectangle1=4*3.5[/tex]
[tex]Rectangle1=14[/tex]
[tex]Rectangle2=5*3.5[/tex]
[tex]Rectangle2=17.5[/tex]
[tex]Rectangle3=3*3.5[/tex]
[tex]Rectangle3=10.5[/tex]
[tex]Triangle1=\frac{4*3}{2}[/tex]
[tex]Triangle1=6[/tex]
[tex]Triangle2=\frac{4*3}{2}[/tex]
[tex]Triangle2=6[/tex]
If you add up all the faces, you get the surface area of the prism:
14+17.5+10.5+6+6=54
When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 56 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 2 batteries do not meet specifications. A shipment contains 7000 batteries, and 1% of them do not meet specifications. What is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?
Answer:
98.1% chance of being accepted
Step-by-step explanation:
Given:
sample size,n=56
acceptance condition= at most 2 batteries do not meet specifications
shipment size=7000
battery percentage in shipment that do not meet specification= 1%
Applying binomial distribution
P(x)=∑ᵇₐ=₀ (n!/a!(n-a)!)p^a (1-p)^(n-a)In this formula, a is the acceptable number of defectives;
n is the sample size;
p is the fraction of defectives in the population.
Now putting the value
a= 2
n=56
p=0.01
[tex]\frac{56!}{0!\left(56-0\right)!}\left(0.01\right)^0\:\left(1-0.01\right)^{\left(56-0\right)} + \frac{56!}{1!\left(56-1\right)!}\left(0.01\right)^1\:\left(1-0.01\right)^{\left(56-1\right)} +[/tex][tex]\:\frac{56!}{2!\left(56-2\right)!}\left(0.01\right)^2\:\left(1-0.01\right)^{\left(56-2\right)}[/tex]
=0.56960+0.32219+0.08949
After summation, we get 0.981 i.e. a 98.1% chance of being accepted. As this is such a high chance, we can expect many of the shipments like this to be accepted!
7. Which two equations are equivalent?
A. y = (x + 3)2 and y = x2 + 6
B. y = (x – 5)2 and y = x2 – 25
c. y = (x – 3)2 and y = x2 - 6x + 9
D. y = (x + 5)2 and y = x2 + 25x + 10
Answer:
C. [tex]y=(x-3)^2[/tex] and [tex]y=x^2-6x+9[/tex]
Step-by-step explanation:
before answering the problem let us remind the formula for square of sum and differences
[tex](a+b)^2=a^2+2 \times a \times b + b^2[/tex]
[tex](a-b)^2=a^2-2 \times a \times b + b^2[/tex]
We are going to use the above two formulas to solve each part and come to an answer
A. [tex]y = (x + 3)^2[/tex]
[tex](x + 3)^2=x^2+2 \times x \times 3 + 3^2[/tex]
[tex](x + 3)^2=x^2+6x+9[/tex]
Hence this option is not correct pair
B. [tex]y = (x-5)^2[/tex]
[tex](x - 5)^2=x^2-2 \times x \times 5 + 5^2[/tex]
[tex](x -5)^2=x^2-10x+25[/tex]
Hence this option is also not correct pair
C. [tex]y = (x -3)^2[/tex]
[tex](x - 3)^2=x^2-2 \times x \times 3 + 3^2[/tex]
[tex](x -3)^2=x^2-6x+9[/tex]
Hence this option is correct as it have equivalent pair
D. [tex]y = (x + 5)^2[/tex]
[tex](x + 5)^2=x^2+2 \times x \times 5 + 5^2[/tex]
[tex](x + 5)^2=x^2+10x+25[/tex]
Hence this option is also not correct pair
What is the value of "c" in the quadratic equation 3x 2 + 5x + 7 = 0?
3
5
7
Answer:
[tex]c=7[/tex]
Step-by-step explanation:
They are just asking you to compare
[tex]ax^2+bx+c=0[/tex] to
[tex]3x^2+5x+7=0[/tex].
What constant values are in the place of [tex]a,b, \text{ and } c[/tex].
[tex]a=3[/tex]
[tex]b=5[/tex]
[tex]c=7[/tex]
Find the slope of the line graphed on the Cartesian plane in the figure.
A. –3⁄4
B. 3⁄4
C. –7⁄2
D. 7⁄2
Answer:
C
Step-by-step explanation:
Multiply.
(x + 7)(3x - 2)
( please answer with
A.
B.
C.
D.
Answer:
A. 3x^2+19x-14
Step-by-step explanation:
Applying the distributive property the given expression is equal to 3x²+19x-14 (Letter A).
Properties of MultiplicationThe properties of multiplication are:
Distributive: a(b±c)= ab±acCommutative: a . b = b. aAssociative: a(b+c)= c(a+b)Identity: b.1=bZero= b*0=0For evaluating the given question, you should apply the distributive property.
The question gives the expression (x+7)(3x-2). Thus, from the distributive property, you have:
3x²-2x+21x-14
3x²+19x-14
From the given options of the question, 3x²+19x-14 is shown in option A.
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Given that a function, g, has a domain of -20 sxs 5 and a range of -5 s g(x) s 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be
true for g.
A g(-4)=-11
B. g(-13) = 20
C. g(7)=-1
D. g(0) = 2
Answer:
s(x) = f(x) + g(x) = (5x + 2) + (7x + 4) = 12x + 6
p(x) = 6*g(x) = 6(7x + 4) = 42x + 24
Step-by-step explanation:
1. does a linear function have to have an x value of 0?
2. what is a constant rate?
3. does a linear function need to be all positive, or can it have some negative values?
Answer:
yes
Step-by-step explanation:
let me explain more in depth. 1: yes, it's the point where the function crosses the x axis. 2: the absence of acceleration. 3: I think it can be negative
NEED HELP WITH A MATH QUESTION
Answer:
87.88 ft^2.
Step-by-step explanation:
Area = 1/2 * base * height
= 1/2 * 16.9 * 10.4
= 87.88 ft^2.
Answer:
87.88 ft²
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here b = 16. 9 and h = 10.4, so
A = 0.5 × 16.9 × 10.4 = 87.88 ft²
a cars fuel efficiency is no less the 45 mpg use F to find the cars fuel efficiency. how do i turn this into an inequality math problem
Answer:
F ≥ 45
Step-by-step explanation:
"No less than" means "greater than or equal to", so you can write the expression as ...
F ≥ 45 . . . . . miles per gallon