Answer:
[tex] - 40 \sqrt{x} [/tex]
Step-by-step explanation:
We want to simplify:
[tex] \sqrt{5} \times - 4 \sqrt{20x} [/tex]
We rewrite the radicand using prime factorization:
[tex] \sqrt{5} \times - 4 \sqrt{4 \times 5x} [/tex]
This gives us
[tex]\sqrt{5} \times - 4 \sqrt{4} \times \sqrt{5} \times \sqrt{x} [/tex]
Create perfect squares and simplify:
[tex](\sqrt{5} )^{2} \times - 4 \sqrt{4} \times \sqrt{x} [/tex]
[tex]5 \times - 4(2) \sqrt{x} [/tex]
[tex]5 \times - 8 \sqrt{x} = - 40 \sqrt{x} [/tex]
Problem Solving
If seven coins add to $1, what
could the coins be?
Answer:
2 quarters and 5 dimes
Step-by-step explanation:
(2) 25 cent coins = 50 cents
(5) 10 cent coins = 50 cents
equals $1
Determine the models that could represent a compound interest account that is growing exponentially.
Select all the correct answers,
A(t) = 2,675(1.003)120
A(t) = 4,170(1.04)
A(t) = 3,500(0.997)4t
A(t) = 5,750(1.0024)20
A(t) = 1,500(0.998)127
A(t) = 2,950(0.999)
Answer: [tex]A(t) = 2,675(1.003)^{120}[/tex]
[tex]A(t) = 4,170(1.04)[/tex]
[tex]A(t) = 5,750(1.0024)^{20}[/tex]
Step-by-step explanation:
The exponential growth equation is given by :-
[tex]y=Ab^x[/tex] , where A = initial value , x= time period , b= growth factor.
The growth factor should be greater than 1.
From all the given options , the equations that are exponential :
[tex]A(t) = 2,675(1.003)^{120}[/tex] , here b= 1.003
[tex]A(t) = 4,170(1.04)[/tex] , here b= 1.04
[tex]A(t) = 3,500(0.997)^{4t}[/tex] , here b= 0.997
[tex]A(t) = 5,750(1.0024)^{20}[/tex] , here b= 1.0024
[tex]A(t) = 1,500(0.998)^{127}[/tex] , here b= 0.998
[tex]A(t) = 2,950(0.999)[/tex] , here b= 0.999
From the above exponential equations , only first , second and fourth equation has b>1.
So , the models that could represent a compound interest account that is growing exponentially. are :
[tex]A(t) = 2,675(1.003)^{120}[/tex]
[tex]A(t) = 4,170(1.04)[/tex]
[tex]A(t) = 5,750(1.0024)^{20}[/tex]
what is this -6=b/18
Answer:
That is math.
Answer:
When only solving for b you would multiple by the reciprocal of 1/18*b so you multiply 18 to both sides and b is equal to -108
Step-by-step explanation:
During the homecoming football game, Quentin lost 20 yards, gained 7 yards, and gained 24 yards in three successive running plays. What was his total gain or loss?
Answer:
He gained 31 yards minus 24 = which is 11 yards.
Step-by-step explanation:
If we gained 24 yards plus the 7 which is 31
So if he loss 20 yards that will be 11 yards left cause 31-24= 11
There's your answer. Hope this helps!
the formula v=u+at is used to find speed of an object. find v if u=6,a=2 and t=5
Answer:
v = 16.
Step-by-step explanation:
This is one of the equations of motion when acceleration is constant.
v = 6 + 2*5
= 16.
Answer: v=16
Step-by-step explanation:
v=6+2(5)
v=6+10
v=16
Select the correct solution set.
50 ≥ 15x
{x | x ≥ 10/3 }
{x | x ≤ 10/3 }
{x | x > 10/3 }
Step-by-step explanation:
[tex]50 \geqslant 15x \\ \\ \implies \: \frac{50}{15} \geqslant x\\ \\ \implies \: \frac{10}{3} \geqslant x \\ \\ \therefore \: x \leqslant \frac{10}{3} \\ thus \: \{x \: | \: x \leqslant \frac{10}{3} \} \: is \: the \: correct \: \\ solution \: set.[/tex]
The correct solution set of 50 ≥ 15x is {x | x ≤ 10/3 }.\
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Given that the expression;
50 ≥ 15x
We can add subtract the 15x - 50 of both sides,
⇒50 - 15x - 50 ≥ 15x -15x - 50
⇒50 - 15x - 50 ≥ 15x -15x - 50
⇒ - 15x ≥ - 50
Now we multiply by -1 ,after this process inequality symbol must be reversed
⇒ 15x ≤ 50
Divide by 50 on both sides,
⇒ 15x / 50 ≤ 50 / 50
⇒ 3x/10 ≤ 1
⇒ x ≤ 10 /3
Therefore, the solution set is {x | x ≤ 10/3 }
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8k - 9 divided by 3 for k = 7/8
Answer:
8k -3 is the answer my boiii
To solve the expression 8k - 9 divided by 3 for k = 7/8, substitute k with 7/8, multiply, subtract 9, and divide by 3 to get the result of -2/3.
Explanation:The student asks to evaluate the expression 8k - 9 divided by 3 for k equals 7/8. Here's how to solve it step-by-step:
First, substitute k with 7/8 into the expression, which results in 8*(7/8) - 9.
Then apply multiplication to the first part: 8 * 7/8, which equals 7.
Next, subtract 9 from 7, yielding -2.
Finally, divide -2 by 3, to get -2/3 as the final result.
Therefore, when k is 7/8, the expression simplifies to -2/3.
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you can buy popcorn at the village theater in small, medium, or large sizes. the pop corn can be buttered or plain. if all the choices are equally likely, what is the probability that a customer chooses a medium size with butter
Answer:
Step-by-step explanation:
Close to none because they are all the same price
The probability of a customer choosing a medium size popcorn with butter is 1/6, or about 16.67%.
To find the probability that a customer chooses a medium size popcorn with butter from the Village Theater, we need to consider the total number of possible outcomes and the number of favorable outcomes. Given there are small, medium, and large sizes, and each can be buttered or plain, there are 3 sizes imes 2 types (buttered or plain), which results in 6 total possible outcomes. The event of choosing a medium size with butter is just one of these possible configurations.
Probability of choosing a medium size with butter = Number of favorable outcomes / Total number of possible outcomes = 1 / 6
The chance is 16.67%, which is the decimal 1/6 expressed as a percentage.
24 + 6 = 6(4 + 2)
What is Jimmy's error?
Jimmy did not write the common factor in the correct place.
Jimmy used 6 as the factor, which is not common to 24 and 6.
Jimmy did not apply the correct operations to the expressions.
Jimmy wrote two expressions that are not equivalent.
Answer:
6 times 2 is 12, 6 times 4 is 24, 30 doesn't equal 36
25 Points!
In the diagram below line FG is // to line HI, and line segments BC and AD intersect a E. The measure of angle GBE=3x+20, and measure angle ECD=x.
Answer:
x = 40
Step-by-step explanation:
Since FG and HI are parallel and BC is a transversal, then
∠ GBE and ∠ GBE are same side interior angles and are supplementary, thus
3x + 20 + x = 180, that is
4x + 20 = 180 ( subtract 20 from both sides )
4x = 160 ( divide both sides by 4 )
x = 40
How many cans will kyra be able to make from the sheet of metal
Kyra will make 9 cans from the sheet of metal.
Solution:
Height of the can (h) = 5 in
Radius of the can (r) = 6 in
The can is in the shape of a cylinder.
Surface area of the cylinder = [tex]2 \pi r^{2}+2 \pi r h[/tex]
Surface area of the can = [tex]2 \times3.14 \times 6^{2}+2 \times 3.14 \times 6\times 5[/tex]
[tex]$=226.08+ 188.57[/tex]
[tex]=414.65[/tex]
Surface area of the can = 414. 65 in²
Area of sheet of metal = 3750 in²
To find how many cans able to make:
[tex]$\text { Number of cans} =\frac{\text { Area of sheet metal }}{\text { Surface area of the can }}[/tex]
[tex]$=\frac{3750}{414.65}[/tex]
= 9.04
Number of cans = 9
Hence Kyra will make 9 cans from the sheet of metal.
U and V are mutually exclusive events. P(U) = 0.27; P(V) = 0.56. Find:
P(U and V) =
b. P(U|V) =
c. P(U or V) =
Answer:
(a) P (U and V) = 0.
(b) P (U|V) = 0.
(c) P (U or V) = 0.83.
Step-by-step explanation:
Mutually exclusive events are those events that cannot occur at the same time. That is, if events A and B are mutually exclusive then,
[tex]P (A\cap B) = 0[/tex]
Given:
Events U and V are mutually exclusive.
P (U) = 0.27 and P (V) = 0.56
(a)
As events U and V are mutually exclusive, the probability of their intersection will be 0.
That is,
[tex]P(U\ and\ V) = P (U\cap V) = 0[/tex]
Thus, the value of P (U and V) is 0.
(b)
The conditional probability of event B given A is:
[tex]P(B|A) =\frac{P(A\cap B)}{P(B)}[/tex]
Compute the value of P (U|V) as follows:
[tex]P(U|V) =\frac{P(U\cap V)}{P(V)}\\=\frac{0}{0.56}\\ =0[/tex]
Thus, the value of P (U|V) is 0.
(c)
The probability of the union of two events, say A and B, is
[tex]P(A\ or\ B)=P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]
Compute the value of P (U or V) as follows:
[tex]P(U\ or\ V)=P(U\cup V)\\=P(U)+P(V)-P(U\cap V)\\=0.27+0.56-0\\=0.83[/tex]
Thus, the value of P (U or V) is 0.83.
The events U and V are mutually exclusive. So, the value of P(U and V) is 0, the value of P(U|V) is 0, and the value of P(U or V) is 0.83 and this can be determined by using the given data.
Given :
P(U) = 0.27P(V) = 0.56U and V are mutually exclusive events.A) P(U and V)
P(U and V) = P(U [tex]\cap[/tex] V) = 0
Because U and V are mutually exclusive events.
B) P(U|V)
[tex]\rm P(U|V) = \dfrac{P(U\cap V)}{P(V)}[/tex]
[tex]\rm P(U|V) = \dfrac{0}{0.56}[/tex]
P(U|V) = 0
C) P(U or V)
[tex]\rm P(U \;or\;V) = P(U\cup V)[/tex]
[tex]\rm P(U \;or\;V) = P(U)+P(V)-P(U\cap V)[/tex]
P(U or V) = 0.27 + 0.56 - 0
P(U or V) = 0.83
The events U and V are mutually exclusive. So, the value of P(U and V) is 0, the value of P(U|V) is 0, and the value of P(U or V) is 0.83 and this can be determined by using the given data.
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for f(x)=2x+1 and g(x)=x^2-7, find (f-g)(x)
(f-g)(x) = [tex]x^{2}[/tex] + 2x + 8
Step-by-step explanation:
Step 1:
Formula for (f-g) (x) = f(x) - g(x)
Step 2:
Substitute values of f(x) and g(x) in the formula and solve
(f-g)(x) = (2x + 1) - ([tex]x^{2} -7[/tex])
(f-g)(x) = 2x + 1 - [tex]x^{2}[/tex] + 7
= 2x + 8 [tex]- x^{2}[/tex]
= [tex]x^{2}[/tex] + 2x + 8
plot points a,b, c and d on a number line so that each statement is true: B < 0, a < c, d > 0, b > c
Answer:
Step-by-step explanation:
what is the solution to the following system?
Answer:
Option C: (2, 1, 0)
Step-by-step explanation:
We are given a system of three equations. Usually, we eliminate a variable from the equations. Solve for the remaining two equations and determine the value of the third equation later.
Here, we are given the choices. So, we can readily substitute each option in the equations. The solution should satisfy all the three equations.
Option A: (3, 1, 0)
Equation (1): 3x + 3y + 6z = 9
⇒ 3(3) + 3(1) + 6(0) = 9 + 3 ≠ 9
Option A does not satisfy the first equation. So, it is eliminated.
Option B: (0, 1, 0)
Substituting in the first equation: 3x + 3y + 6z = 9
⇒ 3(0) + 3(1) + 6(0) = 3 ≠ 9
Option B does not satisfy as well. Hence, it is eliminated.
Option C: (2, 1, 0)
Substituting in 3x + 3y + 6z = 9
⇒ 3(2) + 3(1) + 6(0) = 9
It satisfies Equation 1. For this to be a solution, it should satisfy all the three equations. So, we check for equation 2 and 3.
Equation 2: x + 3y + 2z = 5
2 + 3(1) + 2(0) = 2 + 3 = 5
Equation 3: 3x + 12y + 12z = 18
3(2) + 12(1) + 12(0) = 6 + 12 = 18
Option C satisfies all the equations. So, it is the solution to the system.
On simple substitution, Option D can be eliminated as well.
Hence, the answer.
what is the value of x?
a.50
b.150
c.30
d.100
Salma received a $70 gift card for a coffee store. She used it in buying some coffee that cost $7.61 per pound. After buying the coffee, she had $39.56 left on her card. How many pounds of coffee did she buy?
Answer:
4 pounds
Step-by-step explanation:
Do 70 - 39.56 = 30.44 To see how much she spent
Do 30.44 / 7.61 = 4 To see how many pounds of coffee she had bought
Answer:
4
Step-by-step explanation:
Amount spent on coffee = 70 - 39.56 = 30.44
One pound costs 7.61, how many will cost 30.44
7.61 : 1 = 30.44 : X
7.61 = 30.44/X
X = 30.44/7.61
X = 4
Mr. Falcone pizza shop offers three sizes of pizza. The small medium and large pizzas have diameters of 8 inches 10 inches 12 inches
Step-by-step explanation:
Given,
The diameter of small pizza = 8 inches,
The diameter of medium pizza = 10 inches and
The diameter of large pizza (d) = 11 inches
To find, the circumference of each size of pizza = ?
We know that,
The circumference of the circle = [tex]2\pi r= \pi d[/tex]
∴ The circumference of small size of pizza = 3.14 × 8 = 25.12 inches
The circumference of medium size of pizza = 3.14 × 10 = 31.4 inches
Also,
The circumference of large size of pizza = 3.14 × 12 = 37.68 inches
Thus, the circumference of small size, medium size and large size of pizzas are 25.12 inches, 31.4 inches and 37.68 inches.
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Which mathematical statement is correct?
Answer:
B is the correct option.
Step-by-step explanation:
Place the values from the given options in equations of f(n) and g(n).
Write the answer of each of the following.
For instance, option A gives:
f(6)= 31
g(6) = 24
Option B gives:
f(7)= 63
g(10)= 36
Option C gives:
f(5)= 15
g(8)=30
Option D gives:
f(5)=15
g(5)=21
Thus option B is correct because f(7) is greater than g(10).
Answer:
B. f(7) > g(10)
Step-by-step explanation:
f(7) = 2⁶ - 1 = 63
g(10) = 3×10 + 6 =36
since 63>36 then f(7) > g(10)
:)
A recipe calls for 1/3 of a cup of milk for 10 cookies. How many cups of milk are needed to make 60 cookies?
Answer:
2 cups
Step-by-step explanation:
1/3 times 6 is 6/3, which is equal to two
Answer:
6/3 cups or simplified 2 cups
Step-by-step explanation:
Which expression is equivalent to 9a1/2b14c3/2?
The given algebraic expression 9a1/2b14c3/2 appears to be a kind of factorization where a, b, c are variables raised to different powers. Unless values for these variables are provided, this expression can't be simplified further.
Explanation:The expression 9a1/2b14c3/2 is considered as a form of factorization in mathematics where a, b, c denote variables, and the numbers 1/2, 14, 3/2 are their respective exponents. In other words, it's a product of the variables 'a', 'b', and 'c' raised to their respective powers. For instance, 'a' is under a square root (as signified by the power of 1/2), 'b' is raised to the power of 14, and 'c' is also under a square root but cubed (a power of 3/2).
Consequently, this expression doesn't seem to have a simpler or equivalent expression because the terms 'a', 'b', and 'c' are likely representing different entities, hence they can't be combined or simplified further. However, should there be values for 'a', 'b', and 'c', it's simply substituted into the expression and calculated accordingly.
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Which system of equations below has exactly one solution?
y=-8x - 6 and y = –8x + 6
y=-8x - 6 and 1/2y = -4x - 3
y=-8x - 6 and y = 8x - 6
y = -8x - 6 and -y = 8x + 6
Answer:
(y = -8x - 6 and y = 8x - 6) will have exactly one solution.
Step-by-step explanation:
1) Check number of solutions for A (using substitution)
y = -8x -6
y = -8x + 6
-8x - 6 = -8x + 6
+8x +8x
0 - 6 = 0 + 6
-6 = 6 (since this is false, it would be no solution)
2) Check number of sultions for B (using substition)
y = -8x - 6
1/2y = -4x -3
y = -8x - 6 (Multiply both sides of second equation by 2 to cancel out fraction on left side)
-8x - 6 = -8x - 6
Since this is the same equation on both sides- when you cancel everything out it will be 0=0, meaning infinite solution
3) Check number of solutions for C (using substition)
y = -8x - 6
y = 8x - 6
-8x - 6 = 8x - 6
+8x +6 = +8x +6
0 = 16x
x=0
The X value for the solution is 0, when we plug in this X value into one of the equations and solve for Y we will be able to get the Y coordinate
y = -8(0) - 6
y = -6
The solution for C will by (0,-6) which is one solution.
4) Check number of solutions for D (using substition)
y = -8x - 6
-y = 8x +6 --> y = -8x -6
muiltiply both sides of second equation by -1 to make the y positive
-8x - 6 = -8x - 6
Since this is the same equation on both sides- when you cancel everything out it will be 0=0, meaning infinite solution
-1/3,-0.2,5/3, 0.4,1.3 in least to greatest
Answer: -0.2, -1/3, 0.4, 1.3, 5/3
Step-by-step explanation:
-1/3 is -.33 and 5/3 is 1.66 and then simply place them in order
1/4 square yards of fabic divided into 8 equally sections. What is the size of each seaction in square yards?
Answer:
The size of each section is[tex]\frac{1}{32}[/tex] square yards
Step-by-step explanation:
Given:
Length of the fabric = 1/4 square yards
To Find:
The size of each section in square yards if divided into 8 equal sections
Solution:
Let the size of each section be x
Then
[tex]x = \frac{\text{length of the fabric}}{8}[/tex]
[tex]x = \frac{\frac{1}{4}}{8}[/tex]
[tex]x = \frac{1}{4} \times \frac {1}{8}[/tex]
[tex]x = \frac{1}{32}[/tex]
Then the length of each section will be [tex]\frac{1}{32}[/tex] square yards
will mark brainlist pls help !! :)
Answer:
B
Step-by-step explanation:
I just had the same paper last night
The Adams family has 10 children. The ratio of boys to girls in the Adams family is 1:1. How many girls are in the Adams family?
Answer:5
Step-by-step explanation:
In the Adams family with 10 children and a boy to girl ratio of 1:1, there are 5 girls.
Explanation:The question asked is about the number of girls in the Adams family which has a total of 10 children and the ratio of boys to girls is given as 1:1. When a ratio is 1:1, that means there is an equal number of each. So in the case of the Adams family, there are equal numbers of boys and girls.
To find the number of girls, we simply divide the total number of children by 2. Therefore, the number of girls in the Adams family is 10 ÷ 2 = 5. So, there are 5 girls in the Adams family.
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Which could be the other dimension of the second photograph?
Answer:
15 inches
Step-by-step explanation:
Since the rectangles are similar then the ratios of corresponding sides are equal.
let x be the other dimension in the second photograph, then
[tex]\frac{4}{10}[/tex] = [tex]\frac{6}{x}[/tex] ( cross- multiply )
4x = 60 ( divide both sides by 4 )
x = 15
Thus the other dimension in the second photograph is 15 inches.
Model and solve the problem. 12 x 1/5
Answer:
2 2/5
Step-by-step explanation:
12 x 1/5 = 2 2/5
10(5g+2h-3)-4(3g-4h+2)
Step-by-step explanation:
[tex]10(5g+2h-3)-4(3g-4h+2) \\ \\ = 50g + 20h - 30 - 12g + 16h - 8 \\ \\ = 50g - 12g + 20h + 16h - 30 - 8 \\ \\ = 38g + 36h - 38[/tex]
Answer:
38(g - 1) + 36h
Step-by-step explanation:
10(5g + 2h - 3) - 4(3g - 4h + 2)
= 50g + 20h - 30 - 12g + 16h - 8
= 38g + 36h - 38
= 38(g - 1) + 36h
How do you convert fraction to percent
Answer: dividing
Step-by-step explanation:
Final answer:
To convert a fraction to a percent, divide the numerator by the denominator to get a decimal, multiply the decimal by 100, and then add the percent symbol (%).
Explanation:
To convert a fraction to a percent, you start by converting the fraction into a decimal. To do this, divide the numerator (the top number) by the denominator (the bottom number). Once you have the decimal, you multiply it by 100 to get the percent value. Finally, append the percent symbol (%) to the number.
Example:
For the fraction 3/4, first convert it to decimal:
Divide 3 by 4 to get 0.75.Multiply 0.75 by 100, which equals 75.So, 3/4 as a percent is 75%.Another way to convert fractions to percent is by finding an equivalent fraction that has 100 as its denominator. Then, simply use the numerator as the percent. If the fraction's denominator is not easily scalable to 100, it is easier to use the decimal method described previously.