Answer:
C) 72 students would like to have their test on Wednesday.
Step-by-step explanation:
Given:
8 students want to take their test on Monday.
5 students want to take their test on Tuesday.
12 students want to take their test on Wednesday.
Divide 150 (total students) by 25 (sampled students) = 6
Multiply 6 by each scenario to find the possible prediction.
8 × 6 = 48 students want to take their test on Monday
5 × 6 = 30 students want to take their test on Tuesday
12 × 6 = 72 students want to take their test on Wednesday.
(-3x^2)*(2x^2-3x^3y+5x^3y)
Answer:
-36x+134xy
Step-by-step explanation:
-3x to the power of 2 is -9x
2x to the power of 2 is 4x
now you have -9x times 4x-3x^3y+5x^3y
3x to the power of 3y is 9xy
5x to the power of 3y is 125xy
now you have: -9x times 4x-9xy+125xy
which is: -36x+9xy+125xy
which is: -36x+134xy
A hair salon charges a fixed rate of $25.00 for a haircut and then an additional $15 for any other services. write a function to model the cost of services there and then determine how many services you had if you were charged $25.
The function is f(x) = 15x + 25 and you would have 6 services if you were charged $25
We know that the hair salon charges a fixed rate of $25.00 for a haircut and then an additional $15 for any other services, therefore:
Let x = number of services, then we can obtain the function as:
f(x) = 15x + 25 (function)
when we further solve the function, we get the answer for how many services one would have if we were charged $25,
f(x) = 15x + 25
115 = 15x + 25
90 = 15x
6 = x
Now, we know that the function is f(x) = 15x + 25 and you would have 6 services if you were charged $25
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the power to which a number or expression is raised
The power to which a number or expression is raised is called the exponent.
1. An exponent is a mathematical notation that represents the power to which a number or expression is raised. It is written as a superscript number or variable placed above and to the right of the base number or expression.
2. The base number or expression is the number or expression that is being multiplied repeatedly by itself, raised to the power of the exponent.
3. The exponent tells us how many times the base number or expression should be multiplied by itself. For example, in the expression \(2^3\), the base is 2 and the exponent is 3. This means that 2 should be multiplied by itself three times: 2 * 2 * 2 = 8.
4. The exponent can be a positive whole number, a negative number, zero, or a fraction. Each of these cases has different interpretations:
- Positive exponent: Indicates repeated multiplication. For example, \(2^4\)means 2 multiplied by itself four times.
- Negative exponent: Indicates the reciprocal of the base raised to the positive exponent. For example, \(2^{-3\) means 1 divided by \(2^3\).
- Zero exponent: Always equals 1. For example, \(2^0\) = 1.
- Fractional exponent: Represents a root. For example, \(4^{(1/2)\)represents the square root of 4.
5. Exponents follow certain mathematical properties, such as the product rule \((a^m * a^n = a^{(m+n)})\), the quotient rule \((a^m / a^n = a^{(m-n)})\), and the power rule \(((a^m)^n = a^{(m*n)})\).
Remember to use these rules and definitions to correctly interpret and evaluate expressions involving exponents.
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write two equivalent fractions for each given fraction 10/4, 2/5, 4,6, 3/8
Answer:
10/4 = 5/2 and 15/6
2/5 = 4/10 and 14/35
4/6 = 2/3 and 6/9
3/8= 6/16 and 9/24
Suppose you borrowed $45,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years. By how much would you reduce the amount you owe in the first year? Select the correct answer. a. $7,594.46 b. $7,600.46 c. $7,618.46 d. $7,612.46 e. $7,606.46
The correct answer is option a. $7,594.46.
To calculate the amount you would reduce the amount you owe in the first year, we can use the formula for the equal installment of a loan. The formula is:
Installment = Principal / Number of Installments + (Principal - Total Repaid) * Interest Rate
In this case, the principal is $45,000, the number of installments is 5, and the interest rate is 8.5%.
Let's calculate the amount you would reduce the amount you owe in the first year:
Installment = $45,000 / 5 + ($45,000 - $0) * 0.085Installment = $9,000 + $3,825
Installment = $12,825
Therefore, you would reduce the amount you owe by $12,825 in the first year.The correct answer is option a. $7,594.46.
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If f'(c) < 0 then f(x) is decreasing and the graph of f(x) is concave down when x = c. True False Question 4 (1 point). A local extreme point of a polynomial function f(x) can only occur when f'(x) = 0. True False Question 5 (1 point) If f'(x) > 0 when x < c and f'(x) < 0 when x > c, then f(x) has a maximum value when x = C. True False
Question 3: True
Question 4: False
Question 5: True
If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c.
This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.
Question 3: If f'(c) < 0 then f(x) is decreasing and the graph of f(x) is concave down when x = c.
True
When the derivative of a function, f'(x), is negative at a point c, it indicates that the function is decreasing at that point. Additionally, if the second derivative, f''(x), exists and is negative at x = c, it implies that the graph of f(x) is concave down at that point.
Question 4: A local extreme point of a polynomial function f(x) can only occur when f'(x) = 0.
False
A local extreme point of a polynomial function can occur when f'(x) = 0, but it is not the only condition. A local extreme point can also occur when f'(x) does not exist (such as at a sharp corner or cusp) or when f'(x) is undefined. Therefore, f'(x) being equal to zero is not the sole requirement for a local extreme point to exist.
Question 5: If f'(x) > 0 when x < c and f'(x) < 0 when x > c, then f(x) has a maximum value when x = c.
True
If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c. This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.
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Question 11.
Solve for x.
Answer:
isn't it 90? it has the box next to it
What is the length of the diagonal from P to Q?
Answer:
The length of the diagonal from P to Q is
\( \sqrt{ {9}^{2} + {12}^{2} + {8}^{2} } = \sqrt{289} = 17\)
5( 10- 8 ) solve using distributive property
Answer:
10
Step-by-step explanation:
Just multiply the 5 to the 10 and -8
50-40
10
Answer:
10
Step-by-step explanation:
5×10= 50
5×8= 40
50-40= 10
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answer:
The angle measures 36
Step-by-step explanation:
180 - (87 + 57)
180 - 144 = 36
Answer:
x = 36
Step-by-step explanation:
A triangle is always a 180 degree angle, so add up all of the angles and subtract it to 180
57 + 87 = 144
180 - 144 = 36
x = 36
Penelope is taking a multiple choice test with a total of 40 points available. Each question is worth exactly 5 points. What would be Penelope's test score (out of 40) if she got 3 questions wrong? What would be her score if she got x x questions wrong
Answer:
see below
Step-by-step explanation:
She got 3 questions wrong
3*5 = 15
She missed 15 points
40-15 = 25
She got 25 points right
25/40 =.625 =62.5%
If she got x questions wrong
5x is the points missed
40 -5x is the points correct
(40-5x)/40 = score
Answer:
25pts
Step-by-step explanation:
Show that the two triangles are similar.
11. The triangles are similar to each other by SAS rule of congruency.
12. The triangles are similar to each other by ASA rule of congruency.
13. The triangles are similar to each other by SSS rule of congruency.
Define similar triangles?Triangles that resemble one another but may not be precisely the same size are said to be comparable triangles. If two objects are similar in shape but have different sizes, they are considered to be comparable.
This indicates that comparable shapes superimpose one another when amplified or demagnified. The term "Similarity" refers to this characteristic of like shapes.
Now in the 1st given figure,
One pair of angles are equal to each other, and the sides of the triangle ACE and BCD are in proportion to each other.
So, we can say that the triangles are similar to each other.
In the 2nd figure,
One pair of angles are equal to each. Another pair is equal to each other as the lines are dissecting each other.
And the side is in equal proportion to each other. So, the triangles are congruent to each other.
In the last figure,
One side of the triangle are parallel to each other.
The other sides are in proportion to each other.
Hence, all the three cases triangles are similar to each other.
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Determine which equation is false, based on the solution set S:{3}.
2t = 6
2(2c + 1) = 14
4m + 5 = 12
8 = 3p − 1
Answer:
4m+5=12
Step-by-step explanation:
4(3)+5#12
right hand side is not equal to left hand side
Answer: 4m+5=12
Step-by-step explanation:
In a flower display, there are spaces for 3 plants. If there are 9 plant options, how many different ways can the plants be arranged? Hint: Are repeats allowed?
There are different consecutive ways that the flowers can be planted:
3,9,15,21 and so on.
Numbers that follow each other in a regular counting order or pattern are called consecutive numbers. They are written sequentially, where the difference between the numbers is fixed and no number in between is skipped.
Given that:
Roses plants in 1st, 2nd, row are:
3,9 ,.....
Since difference between consecutive terms is same:
It is an AP
We have to find number of row in the flower bed:
Lets assume there are n rows in the flowers bed.
We know that:
aₙ = a + (n-1)d
and d = 9-3 = 6
Therefore, the next numbers can be:
3,9,15 ,21 ......
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Is 435 a term in the sequence 3,11,19 …? If so, which term is it?
can someone help me with prombelm number 2
Answer:
Work shown below!
Step-by-step explanation:
2. \(g(x)=\frac{1}{2}x+5\)
\(g(4) =\frac{1}{2}*\frac{4}{1} +5= 2+5=7\)
\(g(-10)=\frac{1}{2}*\frac{-10}{1}+5=-5+5=0\)
\(g(0)=\frac{1}{2} *\frac{0}{1} +5=0+5=5\)
Michael is purchasing back to school supplies. He gets a math workbook for $19.88, a calculator for $35.97, and 3 packs of pencils for $3.24 each. How much did he spend on school supplies?
2. Which fraction is not equivalent to 25%?
(EXPLAIN WHY)
1/4
2/5
5/20
25/100
Answer:
The fraction that is not equivalent to 25% is 2/5.
To see why, we can start by converting 25% to a fraction. Recall that "percent" means "per hundred," so 25% is equal to 25/100 or 1/4.
Now, we can check each of the answer choices to see if they are equivalent to 1/4:
1/4 is already in the form of 1/4, so it is equivalent to 25%.
5/20 can be simplified by dividing both the numerator and denominator by 5, which gives 1/4. So 5/20 is also equivalent to 25%.
25/100 is the same as 1/4 (we converted 25% to 1/4 earlier), so it is equivalent to 25%.
This leaves us with 2/5 as the answer choice that is not equivalent to 25%. We can see this by converting 2/5 to a percent:
2/5 = 0.4
0.4 x 100% = 40%
So 2/5 is equivalent to 40%, which is not the same as 25%.
Answer: \(2/5\) second option
Step-by-step explanation: 1/4 is equal to 25% because if you multiply by 100 and divide by 4 that will equal 25. 5/20 simplified to 1/4 which we know is 25%, 25/100 also does too. Therefore, the answer is 2/5 because it simplifies to 40% which isn't 25%.
from 1980 to 1990, the consumer price index
Answer:
1.51
Step-by-step explanation:
If it wrong i'm sorry
i
need the FA3 for L1 + L2
and FA1 for L1
FA1 for L1 FA1 a a 1+ FA2 for L2 FA2 3 a CO b b b b b a a 2 a 4 OS + b
The given expression has to be expanded and evaluated. The given expression is FA1 for\(L1 FA1 a a 1+ FA2 for L2 FA2 3 a CO b b b b b a a 2 a 4 OS + b.\)
\(FA3 for L1 + L2\):
It is given that FA1 for \(L1 = a + b, FA1 a a 1 = 2a\), FA2 for\(L2 = 3a + 4b, FA2 3 a CO b b b b b a a 2 a 4 OS = 3a + 5b\). Substituting the given values in the expression, we have:
\(FA3 for L1 + L2 = (FA1 for L1) (FA1 a a 1) + (FA2 for L2) (FA2 3 a CO b b b b b a a 2 a 4 OS) + b\)
\(FA3 for L1 + L2 = (a + b) (2a) + (3a + 4b) (3a + 5b) + b\)
\(FA3 for L1 + L2 = 2a2 + 3a2 + 15ab + 12b2 + 2ab + b\)
\(FA3 for L1 + L2 = 5a2 + 17ab + 12b2 + b\)
\(FA3 for L1 + L2 is 5a2 + 17ab + 12b2 + b.\)
FA1 for L1:
It is given that FA1 for\(L1 = a + b.\)
FA1 for L1 is a + b.
Answer:
FA3 for L1 + L2 is 5a² + 17ab + 12b² + b and FA1 for L1 is a + b.
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Okkkkkkkkkkkkkkkkkkkkkkkkkkkk
Answer:
GCHE
Step-by-step explanation:
Answer and Explanation:
Problem 1:
4x - 12 = 16
4x = 28
x = 28 / 4
x = 7, G
Problem 2:
5x + 10 = - 25
5x = - 35
x = - 35 / 5
x = -7, C
Problem 3:
x / 2 + 11 = 12
x / 2 = 12 - 11 = 1
x = 2 * 1
x = 2, H
Problem 4:
7.5 * x + 10 = -5
x = -2, E
(Not sure about this one)
Code: GCHE
what does eight 3s mean?
Answer:
8 + 8 + 8 =
Step-by-step explanation:
Thirds are when your timing a number three times.
The eight 3s means that the number 3 is repeated eight times.
A set of symbols and guidelines used to represent and work with numbers is known as a number system. The decimal system, which bases itself on the value of 10, is the most widely used number system.
It employs the symbols 0 through 9 to represent numbers. But, there are a lot more number systems that have been created over time and are still employed in a variety of mathematics, computer science, and engineering sectors.
Eight 3s typically means the number 3 is repeated eight times. In mathematical notation, it is often represented as:
33333333
Therefore, the eight 3s means that the number 3 is repeated eight times.
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Pls help quick
the
A garden store bought a fountain at a cost of $995. 66 and marked it up 100%. Later on,
store marked it down 25%. What was the discount price?
hope it really helps......!!!!!
x -1 0 1 2 h(x) 4 12 36 108write an exponential function of the form y=ab^x
Answer:
\(y=12(3)^x\)Explanation:
Given the form of the exponential function:
\(y=ab^x\)In the pair: (0,12)
\(\begin{gathered} x=0,y=12 \\ \implies12=a\times b^0 \\ \implies12=a\times1 \\ a=12 \end{gathered}\)Substituting a=12, and the point (1,36):
\(\begin{gathered} y=ab^x \\ 36=12\times b^1 \\ 12b=36 \\ b=\frac{36}{12} \\ b=3 \end{gathered}\)Thus, the exponential function is:
\(y=12(3)^x\)I need help with the answer to this question.
9 - 3 divided by 1/3 + 1 = ?
Will give the ranking thing to best explanation.
(sry I don’t know the name of what the ranking is called)
19
Explanation:
9-3=6
(Check your work)
3+6=9
__________________________________
6÷1/3=18
(Check your work)
(6×3=18)
__________________________________
18+1=19
Therefore,
the answer is 19!
what are the common denominators for 2/12 and 7/8
plz help
I need the answer for -3x-3=4x+3
Answer:
\(\huge\boxed{x=-\frac{6}7}\)
Step-by-step explanation:
To solve this problem, use the fact that you can perform any operation(with a few exceptions) to both sides of an equation, to isolate the variable.
Simply subtract 3 from both sides to get:
-3x - 3 - 3 = 4x + 3 - 3
-3x - 6 = 4x
Then add 3x to both sides to get:
-3x + 3x - 6 = 4x + 3x
-6 = 7x
Then divide both sides by 7 to get:
-6 / 7 = 7x / 7
-6/7 = x
Hope it helps :) and let me know if you want me to elaborate
Answer:
-6/7
Step-by-step explanation:
You can use your calulater
step 1: turn it on
Step 2: press 2nd button
step 3: press the number-solve button
step 4:type the equations just like it is writed
Step 5: usef<>d button
and you get your answer -6/7
Point A is at (3, 4) and point M is at (1, 0). Point M is the midpoint of segment AB. What
are the coordinates of Point B
Answer:
B (-1 , -4)
Step-by-step explanation:
A (3 , 4)
M (1 , 0)
\(B\left( x_{B},y_{B}\right)\)
M is the midpoint of segment AB means :
\(\begin{cases}\frac{x_{A}+x_{B}}{2} =x_{M}&\\ \frac{y_{A}+y_{B}}{2} =y_{M}}{} &\end{cases}\)
Then
\(\begin{cases}x_{B}=2x_{M}-x_{A}&\\ y_{B}=2y_{M}-y_{A}&\end{cases}\)
Then
\(\begin{cases}x_{B}=2\left( 1\right) -3&\\ y_{B}=2(0)-4&\end{cases}\)
Then
\(\begin{cases}x_{B}=-1&\\ y_{B}=-4&\end{cases}\)
Simplify the expression below. 2x - 10 + 6x
Answer:
8x - 10
Step-by-step explanation:
Combine like terms:
2x + 6x - 10
= 8x -10
Helen and Stephen both simplify the exponential expression 4 ln21 3 e −
Stephen makes the mistake in the expression as he uses the 4 in the root and the 3 in the power and the expression actually is: ∛(16)/e
How to illustrate the information?We start with the expression:
exp( (4/3)*ln(2) - 1)
Here we can use that:
exp(ln(x)) = x.
and e^(a + b) = e^a*e^b.
the first step here is:
e^((4/3)*ln(2) - 1) = e^((4/3)*ln(2)*e^(-1)
So the first step of Stephen is correct, but the first step of Helen is not, you can not simplify the expression in that way.
now, we have that:
a*ln(x) = ln(x^a)
then we can write:
(4/3)*ln(2) = ln(2^(4/3))
and e^(ln(2^(4/3)) = 2^(4/3)
then we have:
e^((4/3)*ln(2)*e^(-1) = 2^(4/3)/e
now we can write this as:
∛(2^4)/e
Here is where Stephen makes the mistake, he uses the 4 in the root and the 3 in the power.
The expression actually is: ∛(16)/e
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