Answer:
x^32
Step-by-step explanation:
Multiply the exponents in (x4)8.
Which of the expressions shown evaluate to negative rational numbers? Select all that apply. Multiple select question. cross out A) ( − 9 ) 4 cross out B) ( − 4 5 ) 3 cross out C) ( − 3 8 ) 2 cross out D) 3 5 − 10 4 cross out E) ( 9 . 8 ) 2 − 10 2
The negative rational numbers are -9/ 4, -20/ 3 . Option A and B
What are rational numbers?A rational number can be defined as a number that is expressed as a fraction where both the numerator and the denominator are integers.
Examples of rational numbers are;
-1/ 2, 3/ 5, 9/ 2 -3/ 5
Given the expressions;
(-9)/ 4 = -9/4(-4 5) /3 = - 20/ 3(-3 8 ) /2 = -24/ 2 = -12(3 5) - 10/ 4 = 15 - 10/ 4 = 5/ 4(9. 8)2 - 10(2) = 72(2) - 20 = 144 - 20 = 124The rational numbers are -9/4 , -20/ 3 , 5/4
Thus, the negative rational numbers are -9/ 4, -20/ 3 . Option A and B
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Find the equation of the line shown.
The equation of the line shown in the diagram is y = 0.5x+0.5.
What is a line?A line is a mark connecting two points.
To calculate the equation of the line, we use the formula below
Formula:
y = mx+c.............. Equation 1Where:
m = Slope of the graphc = Intercept on the vertical axis.From the diagram,
Given:
m = 1/2 = 0.5c = 0.5Substitute these values into equation 1
y = 0.5x+0.5Hence, the equation of the line shown in the diagram is y = 0.5x+0.5.
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Write a system of equations to describe the
situation below.
Turner is building bookshelves to sell at a furniture
store. First, he built 8 small bookshelves and 3 large
bookshelves, using a total of 369 nails. Later, he built
10 small bookshelves and 10 large bookshelves, using
a total of 780 nails.
Answer:
8x + 3y = 369
10x + 10y = 780
Step-by-step explanation:
x = small bookshelves
y = large bookshelves
8x + 3y = 369
10x + 10y = 780
The length of a rectangle is four meters less than twice its width. If the perimeter of the rectangle is 88 meters, what is the width?
A. 24m
B. 16m
C. 32m
D. 8m
The width of the rectangle is determined as: B. 16 m.
How to Determine the Measurement of a Rectangle?The perimeter of a rectangle = 2(l + w)
l = length of the rectanglew = width of the rectangleGiven the parameters:
Perimeter of rectangle = 88 meters
Width of the rectangle = w meters
Length = 2w - 4 meters
Plug in the values into the perimeter formula of a rectangle
2(2w - 4 + w) = 88
2(3w - 4) = 88
6w - 8 = 88
6w = 88 + 8
6w = 96
6w/6 = 96/6
w = 16
Thus, the width of the rectangle is determined as: B. 16 m.
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the 5th term of an A.P is 9 and the 8th term is 27.Find the 31st term
Answer:
189
Step-by-step explanation:
The difference between consecutive terms of an arithmetic sequence, known as the common difference is given by
d = a(k) - a(k-1) where k = 1,2,3 ....n
We have the 5th term as a(5) = 9
The 6th term is 9 + d
The 7th term is 9 + 2d
The 8th term is 9 + 3d
Each successive term adds a d to the previous term
We have 8th term = 27
So 9 + 3d = 27
3d = 27 - 9 (subtract 9 from both sides)
3d = 18
Divide above by 3 on both sides to get
d = 18/3 = 6
So the common difference is 6
Let's figure out how to calculate the 31st term
We can see that the 5th term can be expressed as
9 + 0d = 9 + 0.6 = 9
The sixth term is
9 + 1d = 9 + 1(6) = 9 + 6 = 15
The seventh term is 9 + 2d = 9 + 12 = 21 and so on
Therefore the general equation for the nth term, given the 5th term
is
a(n) = a(5) + (n - 5)(6) 9 + 6(n - 5)
So the 31st term is
a(31) = 9 + 6(31-1) 9 + 6 x 30 = 9 + 180 = 189
Answer: 31st term is 189
I'd like 75% of my order to be 3 cupcakes and the rest cookies.
How many cookies do I get?
Answer:
1 cookie
Step-by-step explanation:
75% = 75/100
75 and 100 are both divisible by 25, therfore the simplified verision is 3/4
[tex]\frac{75}{100} /\frac{25}{25} =\frac{3}{4}[/tex]
in order to get 100% we would need to:
3/4 + num of cookies = 4/4
re-arranged by subtracting 3/4 on bith sides:
num of cookie = 4/4 - 3/4
num of cookie = 1/4
meaning 1/4 of her orders is cookies
Johnathan worked 4 hours on Monday, 4 hours on Tuesday, 4 hours on Wednesday, 4 hours on Thursday, and 4 hours on Friday. He makes $12.125 an hour. What is his total pay?
Answer:
$242.50
Step-by-step explanation:
The total of number of hours = 20
Hourly pay = 12.125
20*12.125
Total pay= 242.50
Create a Box and Whisker Plot using the following data: 13, 16,
17, 19, 23, 24, 25, 27, 30, 32, 35. What is the median of the set
of data?
24 is the median number because it is found to be at the Middle of all digits
Each side of a square is lengthened by 2 inches. The area of
this new, larger square is 36 square inches. Find the length of
a side of the original square.
Please help using systems of equations!!
Answer:
4 inches.
Step-by-step explanation:
Since the shape is a square, each side length will be the same. This mean that you must find the square root of 36 to find the length of each side of the new square.
√36=6
Each side of the new square is 6. It says it was lengthened by 2 inches. Subtract 2 from 6.
6-2=4
Each side of the original square is 4 inches.
Hope this helps!
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Atsu and Sabu shared an amount of money in the ratio 3:7 respectively. if Sabu received 20 cedis more than Atsu, how much was shared
Answer:
Step-by-step explanation:
Atsu : Sabu
3 : 7
x : x + 20
x is equal to the number of cedis
cross multiply the ratio above
3(x+20) = 7x
3x + (20×3) = 7x
3x + 60 = 7x
3x - 3x + 60 = 7x - 3x (put - 3x on both sides of the equation)
60 = 4x
60/4 = 4x/4 (divide both sides by 4)
15 = x
Daniel makes $2,365 a month plus some money by commission. He gets 5% of everything he sells. If he sold $13,600 worth of items this month, what is his salary for the month?
Study the food web below and answer the following :
i. In the pyramid of numbers there is an increase in numbers towards the base. Mention a pyramid where the base will be smaller.
ii. Predict the impact of removing snakes from this food web
Answer:
predict the impact of removing snakes from this food web
Which driver's race times were the most variable if Driver A has a mean of 4.01 seconds and a standard deviation of 0.05 seconds and Driver B has a mean of 3.96 seconds and a standard deviation of 0.12 seconds and Driver C has a mean of 3.99 seconds and a standard deviation of 0.19 seconds?
The driver B has the fastest typical race time.
It is required to find which driver's race times were the most variable.
What is a statement?A statement is a declarative sentence that is either true or false but not both. A statement is sometimes called a proposition. The key is that there must be no ambiguity. To be a statement, a sentence must be true or false, and it cannot be both.
Given:
From the options presented, driver B has the fastest typical race time because he recorded the smallest time taken to complete an individual race.
Also from the standard deviation given 3.96 seconds for driver B, it shows that the individual time spread from the standard deviation is minimal and that the driver maintained a fairly consistent time of race throughout the racing period.
Therefore, the driver B has the fastest typical race time.
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The sum of two numbers is 72. The difference of the two numbers is 40. What are the two numbers.
Let
x
be the larger number and
y
be the smaller number.
Write an equation that expresses the information in the sentence "The sum of two numbers is 72."
Step-by-step explanation:
x + y = 72
x - y = 40
x = y + 40
so, the first equation is then
y + 40 + y = 72
2y + 40 = 72
2y = 32
y = 16
x = y + 40 = 16 + 40 = 56
Given h(x) = 4x + 2, find h(5).
Answer:
22
Step-by-step explanation:
Simply substitute x = 5 in the function equation
h(5) = 4 (5) + 2 = 20 + 2 = 22
Given ~
[tex] \tt \: h(x) = 4x + 2[/tex]
[tex] \: [/tex]
put the value of x = 5 in given function ~
[tex] \tt \: h(5) = 4(5) + 2[/tex]
[tex] \: [/tex]
[tex] \tt \: h(5) = 20 + 2[/tex]
[tex] \: [/tex]
[tex] \underline{ \boxed{ \tt\red{h(5) = 22}}}{ \green ✓}[/tex]
[tex] \: [/tex]
hope helps ~
To rent a bike (r), kyre pays the flat rate of 5 pesos plus an hourly rental fee (f) of 2 pesos and 50 centavos
The cost of renting the bike will rise at a rate of (B) $2.5 per hour as the number of rent hours increases.
What is a linear function?A linear function represents a straight line on the coordinate plane.The slope of a linear function is always the same and constant.A linear function, in other words, is one that varies linearly with respect to a changing variable.To find what is the rate of change in the cost to rent the bike with respect to the number of rent hours:
The rate of change is also known as the function's slope.Because it is a linear function, the slope will be constant.Slope = difference in ys coordinate/difference in xs coordinateSlope = (30-5)/(10-0) = 2.5Therefore, the cost of renting the bike will rise at a rate of (B) $2.5 per hour as the number of rent hours increases.
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The correct question is given below:
To rent a bike, Max pays a flat rate of $5 plus an hourly rental fee. The graph shows the amount, C, in dollars, that Max pays based on the number of hours, t, that Max rents the bike. What is the rate of change in the cost to rent the bike with respect to the number of rental hours?
(A) $5 per hour
(B) $2.50 per hour
(C) $2 per hour
(D) $7.50 per hour
Write these fractions as powers of ten:
1/1000 7/100 000 1/10000000 3/60000
The fractions represented as power of ten are:
a. 1×(10)⁻³
b. 7× (10)⁻⁵
c. 1 × (10)⁻⁶
d. 5 × (10)⁻⁵
Given :
a. 1/1000
we know that 1/(10)³
when we take the reciprocal, the sign changes from positive to negative.
that is, 1×(10)⁻³
b. 7/100000
we know that 7/(10)⁵
likewise, we get
that is, 1×(10)⁻⁵
c. 1/10000000
we know that 1/(10)⁷
reciprocate it, we get
1×(10)⁻⁷
d. 3/60000
rearrange it.
3/6×10000
divide it.
1/2×10000
divide and multiply by 10.
10/2×10000×10
multiply it.
5/100000
5 × (10)⁻⁵
Hence we calculated the given fractions as powers of ten.
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In a recent year, 17.3% of all registered doctors were female. If there were 41,400 female registered doctors that year, what was the total number of registered doctors?
Round your answer to the nearest whole number.
Answer: 239,306 total registered doctors
Step-by-step explanation:
1. Form the ratio of amount of female doctors(41,400) to total amount of doctors(x) and compare it to percent of female doctors in the field(17.3) to total percent of doctors(100).
[tex]\frac{41400}{x}=\frac{17.3}{100}[/tex]
2. Cross Multiply the amount of female doctors(41,400) to the total percent of doctors(100) so that it stays equal to the percent of female doctors(17.3) to the amount of doctors(x).
[tex]41400*100 = 17.3x[/tex]
3. Simplify
Start by multiplying the amount of female doctors(41,400) by the total percent(100) to get 4.240.000 to keep both sides equal[tex]414*10^{4} = 17.3x[/tex]Then apply the division property of equality by dividing both sides of the equality by the percent of female doctors to the amount of doctors(17.3).[tex]\frac{414*10^{4} }{17.3} = \frac{17.3x}{17.3}[/tex]
After dividing both sides by 17.3 you will find out that there are about 239,306 registered doctors.A seller leaves a buyer approximately one half of a tank of heating oil at the closing. if the tank measures 4' x 2' x 3', how many cubic feet did the buyer receive?
The answer is 12 cubic feet
In mapping diagram D, what is the range?
The range of the relation that is represented in the mapping shown in the diagram attached below is: {3, 5, 11, 21}.
What is the range of a Relation?If we are given a mapping that represents a relation, the input values (x-values) make up the domain of the relation while the output values (y-values) make up the range of the relation.
In the mapping shown in the diagram attached below, we have the following:
The domain of the relation is: {-1, 0, 1, 2, 3}
The range of the relation is: {3, 5, 11, 21}
Thus, we can conclude that, the range of the relation that is represented in the mapping shown in the diagram attached below is: {3, 5, 11, 21}.
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Use the graph to complete each statement. Drag tiles to complete the statements.
Answer: A=ellen B=Dion C=Corey D= Alex E= Corey F=Ellen
Step-by-step explanation:
A teacher claims that the relationship between
number of hours studied for a test and test score can be
described by g(x) = 45 + 9x, where x represents the
number of hours studied. Graph this function
The graph representing the given function g(x) = 45 + 9x is as drawn in the attachment.
How to draw a Linear Equation Graph?
We are given the equation of line as;
g(x) = 45 + 9x
Where;
x represents the number of hours studied.
g(x) represents the test score
Thus, to plot this graph, we need to input some x values and find their corresponding g(x) values
At x = -10;
g(x) = 45 + 9(-10)
g(x) = -45
At x = -1;
g(x) = 45 + 9(-1)
g(x) = 35
At x = 0;
g(x) = 45 + 9(0)
g(x) = 45
At x = 1;
g(x) = 45 + 9(1)
g(x) = 54
At x = 2;
g(x) = 45 + 9(2)
g(x) = 63
At x = 3;
g(x) = 45 + 9(3)
g(x) = 72
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What value of n makes a true statement? 4^nx4² = 16,384
Help please I don’t understand it What is the sum of these questions?
1.X - 10=-9
2.X + 10 = -3
3.x- 3 = 4
4. x / 5 =2
5.22= -11k
6.-13m = -377
7.b - 7= -1
8.-8 = p - 13
9.-40 = -5p
10.-2 = m / 16
I need some help since I don't comprehend what you're asking.
1. A(x) = (f(x)-f(a)) / (x-a) This average rate of change function is called A. The function f's input is represented by x minus a, while the function f's response to the input changing from a to x is represented by f(x) minus f(a).
f(5)=-2 f(9)=14 (f(5)-f(9))/(5-9)=(-2-14)/-4=4 from the table.
Over the range of x = 5 to x = 9, the average rate of change is 4.
2. g(x)=2x2+13x+1, f(x)=4x2+6x
(f/g)(x)=(4x²+6x)/(2x²+13x+1)
Using the numbers shown in the table, x = 4,5,6,7,8,9 and f(x) = 88,85,155,116,180,151,238.190,304,233,378.280
3. f(x)=x2-6x+8, g(x)=x-2, x2-6x-x+8+2=0, x2-7x+10=0 f(x)=g(x)x2-6x+8=x-2x2-6x-x+8+2=0
x₁,₂=(7⁺₋√(7²-4*10))/2=(7⁺₋3)/2 x₁=5, x₂=2
Because 2 doesn't appear in the table of values, the answer using the table of values is x=5.
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Write the equation using y=mx+b
We cannot write vertical lines in the format y = mx+b
This is because the slope of any vertical line is undefined.
The equation of this red line is x = 5. All points on this line have the same x coordinate of 5. Two such points being (5,0) and (5,1)
A 10-lb bag of flour costs $3.69. A 5-lb bag costs $1.55. How much can you save if you buy the big bag instead of 2 small bags?
You will $0.29, if you will purchase 2 small bags of flour instead of 1 big bag.
What exactly is the unitary method?The unitary method is an approach that calculates the value of a specific unit utilizing the values of multiple units, in addition to determining the value of multiple units based on the value of a single unit.To figure out the value of one item, we must first divide it, and then multiply it by the number of things we want to find the value of.For the given question;
The total cost of one big bag that is 10-lb bag of flour = $3.69.
Now, the cost of one small bag that is 5-lb = $1.55.
Thus, the cost for two small bag that is 5-lb = $3.10.
The difference in the cost = big bag cost - 2 small bag costs.
The difference in the cost = $3.69 - $3.10
The difference in the cost = $0.29.
Thus, you will save $0.29 for the purchase of 2 small bags of floor instead of one big bag.
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45h + 1895 = 5000
What is the value of H
Answer:
69
Step-by-step explanation:
45*69+1895=5000
Answer:
h = 69
Step-by-step explanation:
45h + 1895 = 5000 ( subtract 1895 from both sides )
45h = 3105 ( divide both sides by 45 )
h = 69
A square room has a floor area of 144 square feet. the hieght of the room is 6 feet what is the area of one wall
The area of one wall of the room is 72 square feet.
What is the area of a square?The area of a square is given by -
A{S} = a²
where -
{a} is side of square.
Given is a square room has a floor area of 144 square feet. The height of the room is 6 feet.
It is given that -
floor area = 144
a² = 144
a = √(144)
a = √(12 x 12)
a = 12
The area of the wall will be equivalent to -
A{W} = h x a
A{W} = 6 x 12
A{W} = 72 square feet.
Therefore, the area of one wall of the room is 72 square feet.
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Determine whether the system is consistent. x1 x2 x3 = 7 x1 - x2 2x3 = 7 2x1 3x3 = 15
The given system is not consistent.
Given system of equations are:
[tex]x_1+x_2+x_3=7\\x_1-x_2+2x_3=7\\2x_1+3x_3=15[/tex]
Here the indeterminants are [tex]x_1,x_2,x_3[/tex]. A system of equations is consistent if it has at least one set of solution values for the indeterminants.
So we try to solve the above system of equations.
Subtracting the first two solutions, we get,
[tex](x_1+x_2+x_3)-(x_1-x_2+2x_3)= 0[/tex]
⇒ [tex]2x_2-x_3=0[/tex]
⇒ [tex]x_3=2x_2[/tex]
Rewriting all the three equations using this substitution,
[tex]x_1+x_2+2x_2=7\\x_1-x_2+4x_2=7\\2x_1+6x_2=15[/tex]
This implies,
[tex]x_1+3x_2=7\\x_1+3x_2=7\\2x_1+6x_2=15[/tex]
Since the first two equations are same, we need to solve the equations,
[tex]x_1+3x_2=7\\2x_1+6x_2=15[/tex]
Multiplying the first equation by 2 and then subtracting, we get,
0 = -1, which is impossible.
So the system has no solutions.
Hence the system is inconsistent.
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The only measure of center that can be found for both quantitative and qualitative data is the.
The only measure of center that can be found for both quantitative and qualitative data is the mode.
What is the mode?The measure of mode can be calculated for both quantitative and qualitative data. When it is unique, the mode is the value that appears the most frequently in a data set, and it, like the median and mean, can be used as a measure of central tendency. However, there are times when there is no mode or when there are multiple modes. When all observed values appear the same number of times in a data set, there is no mode. To find the mode, arrange the numbers (this makes counting easier), then count how many of each number there are. A mode is a number that appears frequently.Therefore, the only measure of center that can be found for both quantitative and qualitative data is the mode.
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