The rectangular
base of a
20ft tall storage unit is shown
below. Which statement is
FALSE?
a)
b)
c)
The area of the
base is 30ft²
The area is 26ft²
The perimeter is
26ft
d) The perimeter is
(3+3)+(10+10)
MD
Th
3ft
Oft
Answer:
The statement that is FALSE is b) "The area is 26ft²".
potassium 42 has a decay rate of 5.5% per hour. in how many hours will the original quantity be halved?
The half-life of Potassium-42 can be calculated using the following formula:
t1/2 = (ln 2) / λ
where t1/2 is the half-life, ln is the natural logarithm, and λ is the decay rate.
Substituting the values given, we get:
t1/2 = (ln 2) / 0.055
t1/2 ≈ 12.6 hours
Therefore, the original quantity of Potassium-42 will be halved in approximately 12.6 hours.
It will take approximately 13.51 hours for the original quantity of potassium 42 to be halved with a decay rate of 5.5% per hour.
How we can understand about how many hours will the original quantity be halved?To find the number of hours it takes for potassium 42 to be halved with a decay rate of 5.5% per hour, we can use the formula:
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Match the term on the left with the equivalent term on the right.
(x)(2)
x/2
5+x
(1/5)x
↑
(x)/5
2x
(1/2)x
5/x
By answering the presented question, we may conclude that the value of the equation is 5/x --> x/5 or (1/5)x
What is equation?In mathematics, an equation is a statement that states the equivalence of two expressions. An equation is made up of two sides separated by an algebraic equation (=).
For example, the argument contends that the phrase "2x Plus 3" equals the number "9." The purpose of equation solving is to identify the value or values of the variable(s) that will make the equation true.
Simple or complicated equations, regular or nonlinear, with one or more components are all possible. For example, in the equation [tex]"x2 + 2x - 3 = 0,"[/tex] the variable x is raised to the second power. Lines are utilized in many areas of mathematics, including algebra, calculus, and geometry.
[tex](x)(2) -- > 2x[/tex]
[tex]x/2 -- > 0.5x or (1/2)x[/tex]
[tex]5+x -- > x+5[/tex]
[tex](1/5)x -- > x/5 or (x \times 0.2)[/tex]
[tex](x)/5 -- > 0.2x or (1/5)x[/tex]
2x --> same as (x)(2)
[tex](1/2)x -- > 0.5x or x/2[/tex]
Therefore, [tex]5/x -- > x/5 or (1/5)x[/tex]
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(3x²y³ + x² - 7x³y²) - (4x³y² - 6y³ + 2x²)
The simplified expression for the given variables is -7x³y² + 3x²y³ + 6y³.
What is order of operation?A set of principles called the algebraic order of operations specifies the order in which mathematical operations should be carried out in order to simplify equations. The following is the order of events:
Operation inside parentheses should come first. Simplify exponential formulas by using exponents.
Division and multiplication should be done from left to right.
Operationally, add and subtract should be done from left to right.
The given expression can be simplifies as follows:
(3x²y³ + x² - 7x³y²) - (4x³y² - 6y³ + 2x²)
= 3x²y³ + x² - 7x³y² - 4x³y² + 6y³ - 2x²
= -7x³y² + 3x²y³ + 6y³
Hence, the simplified expression is -7x³y² + 3x²y³ + 6y³.
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Note that A, B, C, and D are single decimal digits (from 0 through 9), although they don't have to be
unique (e.g., B and D could be equal). AB is then a two-digit decimal integer, BA is its reverse, and
CDC is a three-digit decimal number
A and B can have values that would give a sum of 11 when they are added together, such as (2,9), (3,8), (4,7), and (5,6).
Here, it is evident that since
AB+ BA= CDC
the hundreds and ones digit of the answer are equal and since we are talking about 2 digit numbers, hundreds place C can only be 1 since it is obtained from carry of the tens place (B+A) and the maximum carry that a 2 digit number can give is 1 (99+99 gives carry 1).
Also, D must be equal to C+1 since it is obtained by B+A and carry of ones place.
C=A+B= 1
D=C+1= 2
The possible values of A and B can be the ones that result in 11 when added, i.e. (2,9),(3,8),(4,7) and (5,6).
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Complete question is attached below
The citizens of a city were asked to choose their favorite pet. The circle graph shows how the citizens answered. If 95,000 citizens answered the question, how many chose
Snakes or Dogs?
fish 13%
dogs 26%
birds 21%
cats 23%
snakes 10%
hamsters 7%
First, we need to calculate the percentage of citizens who chose either Snakes or Dogs.
The percentage of citizens who chose Dogs is 26%, which is equivalent to 0.26 as a decimal.
The percentage of citizens who chose Snakes is 10%, which is equivalent to 0.10 as a decimal.
To find the number of citizens who chose either Snakes or Dogs, we need to multiply the total number of citizens by the combined percentage of Snakes and Dogs:
0.26 + 0.10 = 0.36
So the combined percentage of Snakes and Dogs is 36%.
To find the number of citizens who chose Snakes or Dogs, we can multiply the total number of citizens by this percentage:
0.36 x 95,000 = 34,200
which of the following statements about the f distribution is false? group of answer choices the f distribution is always a left-tailed test. the f distribution is skewed to the right. the f statistic is greater than or equal to zero. as the degrees of freedom of for the numerator or denominator get larger, the curves approximates the normal distribution.
The statement that the f distribution is always a left-tailed test is false statement about the f distribution. So, the right choice for answer option (a).
The F distribution (Snedecor's F distribution) represents continuous probability distribution which occurs frequently as null distribution of test statistics. Let two independent
chi-square variables are x and y with n₁ and n₂ with degree of freedom respectively. So, F-distribution is defined as F = ( X/n₁)/ (Y/n₂)
Characteristics : The F random variable is non-negative variable and the distribution is skewed to the right.
The sampling distribution of F statistic does not involve any population parameters and depends only the degreFor large degrees of freedom n₁ & n₂. F tends to Normal distribution.The Available F tables gives the critical values of F for right-tailed test. P(F > Fx (n₁, n₂)) = αThe F for left tail test both right-tailed &left tailed. So, the false statement is option(a).
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Complete question:
which of the following statements about the f distribution is false? group of answer choices
a) the f distribution is always a left-tailed test.
b) the f distribution is skewed to the right.
c)the f statistic is greater than or equal to zero.
d) as the degrees of freedom of for the numerator or denominator get larger, the curves approximates the normal distribution.
The ratio of girls to boys on team 6-5 is 4:5. If there are 99 students, how many boys are there
Answer:
There are 55 boys.
Step-by-step explanation:
The ratio of
girls: boys:total
4 5 4+5
4 5 9
The total is 99
To get from 9 to 99, we multiply by 11.
girls: boys:total
4*11 5*11 9*11
44 55 99
There are 55 boys.
Find the value of x, y and z
The values of x, y, and z in the given rhombus are: x = -31, y = 20, z = -87.
What do you mean by Equation ?An equation is a mathematical statement saying that two amounts or values are the same, for example 6 x4=12x
We know that the side of a rhombus are equal in length.therefore we can solve the given equation
4y + 8 = -3x - 5 = -z + 1 = 88
Solving each equation for the variables, we get:
4y + 8 = 88
4y = 80
y = 20
-3x - 5 = 88
-3x = 93
x = -31
-z + 1 = 88
-z = 87
z = -87
Heance , the values of x, y, and z in the given rhombus are:
x = -31, y = 20, z = -87.
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Mia buys 50 coats at $28 each.
She sells 38 of these coats at $49 each.
She sells the rest of the coats at $40 each.
Find the overall percentage profit Mia has made on these coats.
Answer: 1264.2857%
Step-by-step explanation:
Answer:
She earned 67.29% profit
Step-by-step explanation:
First let's find how much she spent on the coats.
50 x $28
$1400
So, her expense was $1400
Now, let's find how much she earned selling these coats.
We know she sold 38 of these coats at $49 each. Let's find how much she earned for these 38 coats.
38 x $49
$1862
She earned $1862 on these 38 coats.
Now, let's find how much she earned on the rest of the coats (50-38 which is 12). We know she sold the remaining for $40 each.
12 x $40
$480
She earned $480 on the rest of the coats.
The total she earned $2342
To find the profit:
Profit= $ Earned - Expenses
Profit= 2342-1400
Profit=$942
The question is asking for the percentage.
To find the percentage, we can use the percentage formula:
[tex]\frac{Profit}{Expense}[/tex] x 100
We know that the profit is $942 and the expense is $1400
(We want to find how much profit she made out of the expense)
[tex]\frac{942}{1400}[/tex] x [tex]\frac{100}{1}[/tex]
If you round your answer, you will get 67.29
Answer: She earned 67.29% profit
Mr. Foster is a librarian at Eastside Library. In examining a random sample of the library's book collection, he found the following.
722 books had no damage,
75 books had minor damage, and
29 books had maior damage.
Based on this sample, how many of the 70,500 books in the collection should Mr. Foster expect to have no damage or minor damage? Round your answer to the nearest whole number. Do not round any intermediate calculations.
The number of books that had no damage or minor damage in the sample is:
722 + 75 = 797
To estimate the number of books in the entire collection that would have no damage or minor damage, we can assume that the proportion of books with no or minor damage in the sample is approximately equal to the proportion of books with no or minor damage in the entire collection.
The proportion of books with no or minor damage in the sample is:
797 / (722 + 75 + 29) = 0.9064
So we can estimate the number of books with no damage or minor damage in the entire collection as:
0.9064 x 70,500 = 63,912.6
Rounding to the nearest whole number, we get:
63,913
SEE PHOTO SOLVE ONLY d NOT OTHERS
What is limit of the function f(x) at x = 1 ?
Answer:
Step-by-step explanation:
[tex]f(x)=\frac{(x-1)(x+1)}{x-1}[/tex]
[tex]=x+1[/tex]
Limit is found by substitution: Limit = 1+1 = 2
a company employs eight people and plans to select a group of five of these employees to receive advanced training. how many ways can the group of five employees be selected?
There are 56 ways to select a group of five employees from the eight employees in the company for advanced training.
To select a group of five employees from a company that employs eight people, you can use the concept of combinations.
A combination is the selection of items from a larger set, where the order of items does not matter.
In this case, we want to choose 5 employees from a group of 8.
The formula for calculating combinations is:
C(n, k) = n! / (k!(n-k)!)
Where n is the total number of items, k is the number of items you want to select, and ! denotes the factorial.
So, for this problem:
n = 8 (total employees)
k = 5 (employees to be selected)
Now, we can plug these values into the formula:
C(8, 5) = 8! / (5!(8-5)!)
C(8, 5) = 8! / (5!3!)
C(8, 5) = (8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / ((5 × 4 × 3 × 2 × 1)(3 × 2 × 1))
C(8, 5) = (8 × 7 × 6) / (3 × 2 × 1)
C(8, 5) = (336) / (6)
C(8, 5) = 56
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jordan's mom bought 7 77 packs of juice boxes for the team to drink after practice. each pack had 8 88 boxes of juice. after the team drank as much juice as they wanted, there were 29 2929 boxes of juice remaining. the team only opened each pack after they drank all the boxes from the pack before. how many packs of juice did the team open? packs
The team opened 4 packs of juice.
How to find opened packs?To find out how many packs of juice the team opened, follow these steps:
1. First, find the total number of juice boxes bought by multiplying the number of packs by the number of boxes in each pack: 7 packs × 8 boxes = 56 boxes.
2. Next, subtract the remaining boxes of juice to find out how many boxes the team drank: 56 boxes - 29 boxes = 27 boxes.
3. Finally, divide the number of boxes the team drank by the number of boxes in each pack to find the number of packs they opened: 27 boxes ÷ 8 boxes = 3.375 packs.
Since they only opened each pack after they drank all the boxes from the pack before, the team opened 4 packs of juice.
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The point (4, -12) is on a circle with center (-2,-4). Write the standard equation of the circle.
(x ?)² + (y ?)² =
the standard equation of the circle is (x + 2)² + (y + 4)²= 100 . we can use The standard equation of a circle with center (h,k) and radius r is:
(x - h)² + (y - k)² = r²
what is standard equation of circle ?
The standard equation of a circle with center (h,k) and radius r where (x,y) are the coordinates of any point on the circle. This equation represents all the points in the plane that are a fixed distance (the radius r) from the center of the circle (h,k).
In the given question,
The standard equation of a circle with center (h,k) and radius r is:
(x - h)² + (y - k)² = r²
In this case, we know that the point (4, -12) is on a circle with center (-2, -4). We also know that the radius of the circle is the distance between the center and the point on the circle, which we can find using the distance formula:
r = √((4 - (-2))² + (-12 - (-4))²)
r = √(6² + (-8)²)
r = √(100)
r = 10
So the equation of the circle is:
(x - (-2))² + (y - (-4))² = 10²
(x + 2)² + (y + 4)² = 100
Therefore, the standard equation of the circle is:
(x + 2)² + (y + 4)²= 100
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Siza reads at a rate of 200 words per minute. Calculate how many minutes it will take her to read 300 words. Give your answer in minutes and seconds.
Answer:
1 minute and 30 seconds.
Step-by-step explanation:
200 words in 1 minute
200/2=100
1minute/2=30 seconds
100+200=300 words
1 minute+ 30 seconds= 1 minute and 30 seconds.
There are many cones with a radius of 7 units the equation v= 6pi h relates the height of the cone in units and the volume of the cone in cubic units complete the table using 3.14 for pi
Completed table is shown below. With this h number, we can calculate the cone's volume as V = (1/3)(72)h[tex]\pi[/tex] = 49/3h[tex]\pi[/tex] = 6[tex]\pi[/tex]h = 131.88.
To complete the table relating the height and volume of cones with a radius of 7 units using the equation[tex]v = 6\pi h[/tex], we need to substitute the radius value of 7 units into the formula for volume and then solve for height.
Height (h) Volume (V)
1 131.88
2 263.76
3 395.64
4 527.52
5 659.4
To obtain volume for each height, we plug in radius value of 7 units into the formula for the volume of a cone, which is given by [tex]V = (1/3)\pi r^{2} h[/tex]. This gives us [tex]V = (1/3)\pi (7^{2} )h = 49/3\pi h[/tex],
which simplifies to V = 16.33h. Then we substitute this expression for V into given equation [tex]v = 6\pi h[/tex] to obtain [tex]16.33h = 6\pi h[/tex], and solve for h to obtain h = 6.56.
Using this value of h, we can obtain the volume of the cone as [tex]V = (1/3)\pi (7x^{2} )h = \\49/3\pi h = \\6\pi h = \\131.88[/tex]
After that, by multiplying the value of h by 16.33 and rounding to two decimal places, we can determine the volumes for the other heights in the table.
Therefore, the completed table is as shown above.
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the billy bob landed on the coordinate plane at (-3,3 ), bertha landed at ( 1,0 ). how far did billy bob land from bertha
Answer:
5 units
Step-by-step explanation:
The distance from -3 to 1 is 4 and the distance from 3 to 0 is 3. Use the Pythagorean Theorem.
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
[tex]4^{2}[/tex] + [tex]3^{2}[/tex] = [tex]c^{2}[/tex]
16 + 9 = [tex]c^{2}[/tex]
25 = [tex]c^{2}[/tex]
[tex]\sqrt{25}[/tex] = [tex]\sqrt{c^{2} }[/tex]
5 = c
Helping in the name of Jesus.
Which of the following can be constructed by drawing an angle on tracing
paper and then folding the paper so that the rays forming the angle lie upon
each other?
A. Parallel lines
B. Perpendicular line segment
C. Angle bisector
D. Median of a line segment
C. Angle bisector can be constructed by drawing an angle on tracing paper and then folding the paper so that the rays forming the angle lie upon each other. When you fold the paper, the crease that is formed will be the angle bisector of the original angle.
can somebody helppp please, do all the tasks from a and b.
Thank u!!!
in photo.
The solutions for the quadratic equations ax² + bx = 0 are:
a) x=0 or x=-2 for x²+2x=0;
x=0 or x=2 for x²-2x=0;
x=0 or x=2 for -x²+2x=0;
x=0 or x=-2 for -x²-2x=0.
b) x=0 or x=-5/3 for 3x²+5x=0;
x=0 or x=5/3 for 3x²-5x=0;
x=0 or x=5/3 for -3x²+5x=0;
x=0 or x=-5/3 for -3x²-5x=0.
How did we get these values?a) To solve the quadratic equations ax² + bx = 0, we need to factor out the common variable x, and then solve for x:
a) x²+2x=0
x(x+2)=0
x=0 or x=-2
b) x²-2x=0
x(x-2)=0
x=0 or x=2
c) -x² + 2x = 0
-x(x-2)=0
x=0 or x=2
d) -x²-2x=0
-x(x+2)=0
x=0 or x=-2
b) To solve the quadratic equations 3x²+5x=0, 3x²-5x=0, -3x²+5x=0, and -3x²-5x=0, we factor out the common variable x and then solve for x:
b) 3x²+5x=0
x(3x+5)=0
x=0 or x=-5/3
b) 3x²-5x=0
x(3x-5)=0
x=0 or x=5/3
c) -3x²+5x=0
x(-3x+5)=0
x=0 or x=5/3
d) -3x²-5x=0
x(-3x-5)=0
x=0 or x=-5/3
Therefore, the solutions for the quadratic equations ax² + bx = 0 are:
a) x=0 or x=-2 for x²+2x=0;
x=0 or x=2 for x²-2x=0;
x=0 or x=2 for -x²+2x=0;
x=0 or x=-2 for -x²-2x=0.
b) x=0 or x=-5/3 for 3x²+5x=0;
x=0 or x=5/3 for 3x²-5x=0;
x=0 or x=5/3 for -3x²+5x=0;
x=0 or x=-5/3 for -3x²-5x=0.
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The English translation of the question in the picture:
75. Solve the quadratic equations ax² + bx = 0
a) x²+2x=0,
x²-2x=0,
-x² + 2x = 0.
-x²-2x=0;
b) 3x²+5x=0,
3x²-5x=0.
-3x²+5x=0,
-3x²-5x=0;
EREGENT PLEASE HURRY DONT LIE
O A. (x, y) - (x - 2, y+ 6)
O B. (x, y) - (x+ 2, y - 6)
O C. (x, y) - (x - 6, y + 2)
O D. (x, y) - (x+ 6, y - 2)
The answer is C. (x,y) - (x - 6, y + 2)
give the percentage of measurements in a data set that are above and below each of the following percentiles. a. th percentile b. th percentile c. th percentile d. th percentile
The percentage of measurements in a data set that are above and below each of the following percentiles are 68%, 95% and 99.7%.
We need to calculate the percentage of the measurements contained in each of the following intervals:
According to the empirical rule, approximately 68% of the measurements in a normally distributed data set will fall within one standard deviation of the mean. Therefore, approximately 68% of the measurements will fall within the interval (mean - s, mean + s).
Similarly, approximately 95% of the measurements in a normally distributed data set will fall within two standard deviations of the mean. Therefore, approximately 95% of the measurements will fall within the interval (mean - 2s, mean + 2s).
Likewise, approximately 99.7% of the measurements in a normally distributed data set will fall within three standard deviations of the mean. Therefore, approximately 99.7% of the measurements will fall within the interval (mean - 3s, mean + 3s).
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Multiply.
(3x-4y) (4x-7y)
Simplify your answer.
Answer:
To multiply (3x - 4y) and (4x - 7y), we need to use the distributive property, which states that: a(b + c) = ab + ac Using this property, we can expand the given expression as: (3x - 4y)(4x - 7y) = 3x(4x) + 3x(-7y) - 4y(4x) - 4y(-7y) Simplifying each term, we get: = 12x^2 - 21xy - 16xy + 28y^2 = 12x^2 - 37xy + 28y^2 Therefore, the simplified answer is 12x^2 - 37xy + 28y^2.
7 students divided by 8 sandwiches. How many pieces of the sandwiches does each student get?
If 7 students divided by 8 sandwiches each student gets 8 pieces of sandwich.
If 7 students are divided by 8 sandwiches, we can start by calculating the total number of pieces of sandwich available:
Total number of pieces of sandwich = 7 * 8 = 56
So there are 56 pieces of sandwich available for 7 students.
To find out how many pieces of sandwich each student gets, we divide the total number of pieces of sandwich by the number of students:
Each student gets 56 / 7 = 8 pieces of sandwich.
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i need to find the product
Answer:
c ik this because I took the same question as you
The product of the given algebraic expression is [tex]\frac{4}{(x-1)}[/tex].
The given expression is [tex]\frac{8x+8}{x^2-2x+1} .\frac{x-1}{2x+2}[/tex].
Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.
Here, [tex]\frac{4(2x+2)}{x^2-1x-1x+1} \times \frac{x-1}{2x+2}[/tex]
= [tex]\frac{4(2x+2)}{x(x-1)-1(x-1)} \times \frac{x-1}{2x+2}[/tex]
= [tex]\frac{4(2x+2)}{(x-1)(x-1)} \times \frac{x-1}{2x+2}[/tex]
Cancel the same factors, that is
= [tex]\frac{4}{(x-1)} \times \frac{1}{1}[/tex]
= [tex]\frac{4}{(x-1)}[/tex]
Therefore, the product of the given algebraic expression is [tex]\frac{4}{(x-1)}[/tex].
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Determine the surface area of a right circular cone that has a slant height of 5.8 ft and a diameter of 6.4 ft? Round your answer to the nearest whole.
After answering the presented question, we can conclude that Rounding this to the nearest whole number, we get a surface area of 91 sq. ft.
What is diameter?In geometry, the diameter of a circle is any straight line segment that has an endpoint on the circle and travels through its centre. Another way to put it is the longest chord of a circle. Either idea can be used to define the diameter of a sphere. The diameter is the length of the line that runs tangent to the two points at either end of the circle. If you take length to be the distance between two points, diameter equals length. The diameter of a circle is the distance between its two furthest points.
First, we need to find the radius of the cone:
[tex]radius = diameter/2 = 6.4/2 = 3.2 ft[/tex]
Now we can use the Pythagorean theorem to find the height of the cone:
[tex]height^2 = slant height^2 - radius^2[/tex]
[tex]height^2 = 5.8^2 - 3.2^2[/tex]
[tex]height^2 = 20.84[/tex]
height ≈ 4.56 ft
Next, we can find the surface area of the cone by adding the area of the base to the lateral surface area. The base is a circle with radius 3.2 ft, so its area is:
base area =[tex]\pi (radius)^2[/tex]
base area =[tex]\pi (3.2)^2[/tex]
base area ≈ 32.17 sq. ft.
The lateral surface area is the curved surface area of the cone, which can be found using the slant height and the radius:
lateral surface area = [tex]\pi (radius)(slant height)[/tex]
lateral surface area = [tex]\pi (3.2)(5.8)[/tex]
lateral surface area ≈ 58.92 sq. ft.
Therefore, the total surface area is:
total surface area ≈ base area + lateral surface area
total surface area ≈ [tex]32.17 + 58.92[/tex]
total surface area ≈ 91.09 sq. ft
Rounding this to the nearest whole number, we get a surface area of 91 sq. ft.
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-8(2x-4) i need help help
Answer:
Therefore, -8(2x-4) simplifies to -16x + 32.
Step-by-step explanation:
-8 * 2x - (-8 * 4)
Simplifying this expression further gives:
-16x + 32
Therefore, -8(2x-4) simplifies to -16x + 32.
Answer:
Step-by-step explanation:
1/2(x-3)(x+5) Find the vertex and write it as an ordered pair
The vertex of the parabola is (-2, -3/2).
First, let's expand the given expression:
[tex]1/2(x-3)(x+5) = 1/2(x^2 + 2x - 15)[/tex]
Now, we can see that the coefficient of[tex]x^2[/tex] is positive, which means the parabola opens upwards.
To find the vertex, we can use the formula:
Vertex = (-b/2a, f(-b/2a))
where a = 1/2, b = 2, and f(x) =[tex]1/2(x^2 + 2x - 15).[/tex]
Substituting the values, we get:
Vertex = (-2/(21/2), f(-2/(21/2))) = (-2, f(-2))
To find f(-2), we can substitute x = -2 in the expression for f(x):
f(x) = [tex]1/2(x^2 + 2x - 15)[/tex]
f(-2) = [tex]1/2((-2)^2 + 2(-2) - 15)[/tex]
= 1/2(-3)
= -3/2
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you run a one-sample z test (z.test) in excel and get the following result: 0.7326 what does the output of 0.7326 represent? group of answer choices the sample value the critical value the one-tailed probability value the significance level
The output of 0.7326 represents the test statistic (Z-score) computed from the 1-sample Z-test in Excel.
It tells you how many standard deviations the sample mean is from the population mean under the null hypothesis.
A test statistic (Z-score) is a numerical value used in statistical hypothesis testing to assess the evidence against the null hypothesis.
A test statistic measures the difference between a sample statistic (eg sample mean) and the corresponding population parameter (eg population mean) assuming the null hypothesis is true.
For the Z-test, the test statistic is computed as
z = (x - μ) / (σ / √n)
where x = sample mean,
μ = population mean,
σ= population standard deviation,
and n = sample size.
The resulting Z-score indicates how many standard deviations the sample mean is from the population mean, assuming the null hypothesis is true.
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