Answer:
Area of the floor of the classroom is 72 inch².
Step-by-step explanation:
We are given the dimensions of the rectangular floor as,
Length = 36 feet and Width = 32 feet
Since, the scale drawing have the length = 9 inches
This gives, the ratio of the actual length to the scale drawing length = [tex]\frac{36}{9}[/tex]
Thus, we have,
[tex]\frac{36}{9}=\frac{32}{x}[/tex], where x is the width in the scale drawing.
So, on solving,
[tex]x=\frac{32\times 9}{36}[/tex] i.e. x= 8 inches
Since, Area of the rectangle= Length × Width
Thus, area of the rectangular floor = 9 × 8 = 72 inch².
Thus, the area of the floor of the classroom is 72 inch².
The area of the floor of the scale drawing and the scale factor are 72 in² and 1/4 respectively
Actual Length = 36 feets Actual width = 32 feets Model width = 9 inchesThe scale factor = 9 / 36 = 1/4
The length of the model canbe calculated thus :
Actual Length × scale factorModel width = 32 × 1/4 = 8 inches
The Area of a rectangle can be calculated using the relation :
Area = Length × widthArea of floor = 8 inches × 9 inches = 72 inch²
Therefore, the area of the floor of the scale drawing is 72 in²
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simplify yhe expression 2(10) + 2( x--4).
3x+6y=-9 and X+2y=-3
[tex]\left\{\begin{array}{ccc}3x+6y=-9&\text{divide both sides by (-3)}\\x+2y=-3\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-x-2y=3\\x+2y=-3\end{array}\right}\qquad\text{add both sides of the equations}\\. \qquad\qquad0=0\qquad TRUE\\\\Answer:\ \boxed{\text{Infinitely many solutions}}\\\\\left\{\begin{array}{ccc}x\in\mathbb{R}\\y=-\dfrac{1}{2}x-\dfrac{3}{2}\end{array}\right[/tex]
Write the equation in slope intercept form: Passes through = (2,3) (0,9)
Answer:
Y=-3x+9
Step-by-step explanation:
Slope is found using
9-3 over 0-2
This gets 6/-2
This gets -3
-3 is the slope
9 is the y-intercept
August hosted two dinner parties for his friends. Twenty guests attended the first party, and twenty-six guests attended the second party. What is the percentage increase of the number of guests from the first party to the second party?
Answer: 30%
Step-by-step explanation:
The first step is to find the increase in numbers
26-20= 6
Now you find the percent. This means you're looking for the percent 6 is equal to when compared to 20. The easiest way is to divide the increase by the original number
6/20= 0.3
To convert that to percent, multiply it by 100
0.3 * 100= 30%
There was a 30% increase.
Final answer:
To calculate the percentage increase of guests from August's first party to the second, subtract the initial number from the final number, divide by the initial number, and multiply by 100. The calculation shows a 30% increase in guests from 20 to 26.
Explanation:
The question asks to calculate the percentage increase in the number of guests from the first dinner party to the second dinner party hosted by August. To find the percentage increase, you subtract the original number of guests from the new number of guests, divide by the original number, and then multiply by 100 to get the percentage.
We start with the initial number of guests at the first party, which is 20, and the final number of guests at the second party, which is 26. Using the formula:
Percentage Increase = ((Final Number - Initial Number) / Initial Number) × 100
Percentage Increase = ((26 - 20) / 20) × 100
Percentage Increase = (6 / 20) × 100
Percentage Increase = 0.3 × 100
Percentage Increase = 30%
Therefore, the percentage increase of the number of guests from the first party to the second party is 30%.
In a auditorium, there are 9 rows of 18 seats in each row. There are also 6 rows of seats with 24 seats in each row. How many seats are in the auditorium? Estimate first. Check for reasonableness.
Answer:
306
Step-by-step explanation:
9 times 18= 162
24 times 6= 144
144+162=306
Kian bought a shirt for $12 and a pair of jeans for $28. If the sales tax rate is 8.5%, what will the total cost of his purchase be after tax ?
Answer:
$43.40
Step-by-step explanation:
12 + 28
40
40 (1.085) <<< sales tax
43.40
Answer: $43.40
Step-by-step explanation:
Total Cost of products (before sales tax): $12 + $28 = $40
After sales tax: ($40 × 108.5%) ÷ 100% = $43.4 = $43.40
Mrs. Green went to a local store to buy a computer that is on sale. The sales tax rate is 7% of the sale price. If Mrs. Green pays a sales tax of $87.50, what is the sales price of the computer?
Need help with Mathematics. I can't copy and paste so I screenshot it
Answer: 1.44
Step-by-step explanation:
1.2×1.2
1.2
1.2
__
24
120
__
144
Add two decimal places: 1.44
Answer:
1.44
Step-by-step explanation:
1.2^2 = 1.2 * 1.2
1.2 * 1.2 = 1.44
Your just finding the squad route of it. It can also be done the same way when your ^3 or even ^4 since its all timing the same number. Hope this helps out!
Simplify.
Write your answer without parentheses.
Answer:
Simplifying the expression eliminating the parentheses:
(-5 u^2 w)^3 = -125 u^6 w^3
Step-by-step explanation:
(-5 u^2 w)^3 = (-5)^3 (u^2)^3 (w)^3
(-5 u^2 w)^3 = (-5)(-5)(-5) u^(2 x 3) w^3
(-5 u^2 w)^3 = -125 u^6 w^3
Sue sold 26 more newspapers than bill, and bill sold three times as many as Harry. If Harry sold p newspapers, how many did Sue sell?
Answer:
3p + 26
Step-by-step explanation:
Let S = Sue's newspapers sold
B = Bill's newspapers sold
H = Harry's newspapers sold.
We have three conditions:
(1) S = B + 26
(2) B = 3H
(3) H = p Substitute (3) into (2)
(4) B = 3p Substitute (4) into (1)
S = 3p + 26
Sue sold 3p + 26 newspapers.
Find two numbers if their difference is 90, and their ratio is 5:8.
Answer:
150 and 240 are the two numbers having difference as 90 and ratio as 5 : 8.
Step-by-step explanation:
Since ratio of two numbers is 5 : 8 ,
lets assume two numbers be 5x and 8x.
Difference of two numbers = 8x - 5x = 90
⇒3x =90
⇒x = 90/3=30
so two numbers are 5x = 5 × 30 = 150 and 8x = 8 × 30 = 240
Hence 150 and 240 are the two numbers having difference as 90 and ratio as 5 : 8.
T-shirts are sold in packages of 4.The store’s 139 employees will each be given 5 t-shirts. How many packages will the store need to order?
Answer:
174 packages of t-shirts PLEASE GIVE BRAINLIEST
Step-by-step explanation:
139 x 5 = 695 t-shirts are needed
695 ÷ 4 = 173.75
Since you have to purchase whole packages of t-shirts you will need to buy 174 packages of t-shirts. 174 x 4 = 696 t-shirts
174 packages
Solve the following subtraction problems. a. 8 mi. 133 yd. 2 ft. – 5 mi. 107 yd. 2 ft. b. 2 yd. 2 ft. 6 in. – 1 ft. 11 in. c. 6 yd. – 2 ft. 7 in. d. 8 yd. 4 in. – 7 yd. 2 ft. 8 in.
Let's keep in mind the conversion factors between mile, yard, feet and inches:
1 mile = 1760 yards
1 yard = 3 feets
1 feet = 12 inches
a) 3 mi. 26 yd.
We have:
8 mi. 133 yd. 2 ft. –
5 mi. 107 yd. 2 ft =
Here, we can simply do the substraction of each term, and we get:
(8-5) mi (133-107) yd (2-2) ft =
3 mi. 26 yd 0 ft =
3 mi. 26 yd.
b) 2 yd. 7 in.
We have:
2 yd. 2 ft. 6 in. –
0 yd. 1 ft. 11 in.
Here, we need to convert 1 feet into 12 inches and add them to the inches in the first term as follows:
2 yd. 2 ft. 6 in. = 2 yd. 1 ft. (6+12) in. = 2 yd. 1 ft. 18 in.
So now the subtraction becomes:
2 yd. 1 ft. 18 in. –
0 yd. 1 ft. 11 in.
and now we can simply do the substraction of each term, and we get:
(2-0) yd. (1-1) ft. (18-11) in. =
2 yd. 0 ft. 7 in. =
2 yd. 7 in.
c) 5 yd. 5 in.
We have:
6 yd. 0 ft. 0 in. –
0 yd. 2 ft. 7 in.
We have to "move" 1 yard into feets and inches in the first term, as follows:
6 yd. 0 ft. 0 in. = 5 yd. 3 ft. 0 in. = 5 yd. 2 ft. 12 in.
And now the subtraction becomes:
5 yd. 2 ft. 12 in. -
0 yd. 2 ft. 7 in. =
5 yd. 0 ft. 5 in. =
5 yd. 5 in.
d) 8 in.
We have:
8 yd. 0 ft. 4 in. –
7 yd. 2 ft. 8 in.
Again, let's convert the first term, moving yards into feets and inches:
8 yd. 0 ft. 4 in. = 7 yd. 3 ft. 4 in. = 7 yd. 2 ft. (4+12) in. = 7 yd. 2 ft. 16 in.
So now the subtraction is:
7 yd. 2 ft. 16 in. -
7 yd. 2 ft. 8 in. =
0 yd. 0 ft. 8 in. =
8 in.
887 is what percent of 4132
Answer:
21.46 or 21.5
Step-by-step explanation:
To find the answer to this problem you must divide 877 by 4132, which gets you 0.2146. Then you multiply this answer by 100 to find the percentage; which in this case is 21.46, or 21.5 if you are rounding up. I hope my answer helped you!
887 is 21.47% of 4132, found by dividing 887 by 4132 and multiplying by 100.
To find out what percent 887 is of 4132, you need to use the formula for calculating percentages, which involves dividing the part by the whole and then multiplying the result by 100.
Here is how you can compute it step-by-step:
Divide 887 by 4132, which gives you approximately 0.2147.
Multiply this result by 100 to convert it into a percentage: 0.2147 * 100 = 21.47%.
Therefore, 887 is 21.47% of 4132.
Which expression will give the new price of a $15 item marked up by 28%
A. 28+0.15 X 28
B. 28-0.15 X 28
C. 15+0.28 X 15
D. 15-0.28 X 15
Answer:
the answer is
C
if i am wrong let me know
Step-by-step explanation:
Error Analysis Mario has 7 cups of milk. A one-batch recipe for pancakes calls for two thirds cup of milk. To see how many batches he could make, Mario finds 7 divided by two thirds . He said that because 7 divided by two thirds equalsone seventh times three halves , he could make three fourteenths of a batch . What was his error? How many batches could he make?
A.
He multiplied the dividend by the divisor.
B.
He multiplied the reciprocal of the dividend by the divisor.
C.
He multiplied the dividend by the reciprocal of the divisor.
D.
He multiplied the reciprocal of the dividend by the reciprocal of the divisor.
[tex]\bf 7\div \cfrac{2}{3}\implies 7\cdot \cfrac{3}{2}\implies \cfrac{7\cdot 3}{2}\implies \cfrac{21}{2}\implies 10\frac{1}{2}~~\checkmark \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{so, what happened to Mario?}}{7\div \cfrac{2}{3}\implies \cfrac{7}{1}\div \cfrac{2}{3}}\implies \stackrel{\boxed{?}}{\cfrac{1}{7}}\cdot \cfrac{3}{2}\implies \cfrac{3}{14}~~\bigotimes[/tex]
he ended up multiplying the 7 by the 2 for some reason.
and an explanation could be he used the reciprocal of both numbers mistakenly.
Answer:
c
Step-by-step explanation:
Which answers describe the end behaviors of the function modeled by the graph? f(x)=4 1/3x+3 , Select each correct answer.
As x decreases without bound, f(x) approaches the line y=3 .
As x increases without bound, f(x) increases without bound.
As x increases without bound, f(x) approaches the line y=3 .
As x increases without bound, f(x) decreases without bound.
Answer:
As x decreases without bound, f(x) approaches the line y=3 .
As x increases without bound, f(x) increases without bound.
Step-by-step explanation:
From the given graph f(x), we can see that
When x increases the value of y also increases
When x decreases the y values goes close to 3 but it does not cross 3
As x goes to positive infinity , y approaches positive infinity
As x increases without bound, f(x) increases without bound.
As x goes to negative infinity, y values approaches +3
As x decreases without bound, f(x) approaches the line y=3
As x decreases without bound, f(x) approaches the line y=3 . As x increases without bound, f(x) increases without bound. Therefore, options A and B are correct answers.
The given function is f(x)=4 1/3x+3.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
From the given graph f(x), we can see that
When x increases the value of y also increases
When x decreases the y values goes close to 3 but it does not cross 3
As x goes to positive infinity, y approaches positive infinity
As x increases without bound, f(x) increases without bound.
As x goes to negative infinity, y values approaches +3
As x decreases without bound, f(x) approaches the line y=3
Therefore, options A and B are correct answers.
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there are 820 people 65% of them are adults and 20% are boys how many girls are there
Answer:
123
Step-by-step explanation:
Assuming that 85% of the total was either adults or boys, we can subtract
100-85
=15
Therefore, that 15% is girls
820*.15
=123
How to write a linear function with the values f(3)=-4 f(5)=-4
To write a linear function with the given values f(3) = -4 and f(5) = -4, we can use the point-slope form of a linear equation. The linear function is y = -4.
Explanation:To write a linear function with the given values f(3) = -4 and f(5) = -4, we can use the point-slope form of a linear equation. The formula for point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. We can choose any point (x1, y1) from the given values. Let's choose (3, -4) as a point on the line. Now we can substitute the values into the formula to find the linear function:
y - (-4) = m(x - 3)
y + 4 = m(x - 3)
To find the slope, we can use another point on the line, such as (5, -4). Substituting the values into the formula, we get:
-4 + 4 = m(5 - 3)
0 = 2m
Solving for m, we get m = 0.
Now we can substitute the slope and one of the points back into the formula to find the linear function:
y + 4 = 0(x - 3)
y + 4 = 0
y = -4
So, the linear function with the given values is y = -4.
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Given values f(3) = -4 and f(5) = -4 suggest a horizontal line as the y-coordinate remains constant at -4 regardless of x values. Hence, the linear function is f(x) = -4.
Explanation:The student wants to know how to write a linear function with the values f(3)=-4 and f(5)=-4. The first thing we need to understand here is that a linear function is represented by the equation y = mx + b, where y is the output, m is the slope, x is the input, and b is the y-intercept. In this problem, since f(3) = -4 and f(5) = -4, it indicates that the y coordinate remains the same (-4), thus forming a horizontal line despite the changes in the x coordinates. This means the function has a slope (m) of 0. So, the linear function that satisfies these conditions is f(x) = -4.
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what is the slope-intercept form for a line that has a slope of -4/5 and passes through points (0,7)?
[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{7})~\hspace{10em} slope = m\implies -\cfrac{4}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-7=-\cfrac{4}{5}(x-0) \\\\\\ y-7=-\cfrac{4}{5}x\implies y=-\cfrac{4}{5}x+7[/tex]
a quantity with an initial value of 2100 decades exponentially at a rate of 0.65% every 10 days what is the value of the quantity after 186 hours to the nearest hundredth
Answer:
The value of the quantity after 186 hours is 2089.41
Step-by-step explanation:
We can use exponential formula
[tex]P(t)=a(1-b)^{\frac{t}{h} }[/tex]
a quantity with an initial value of 2100
so,
[tex]a=2100[/tex]
decays exponentially at a rate of 0.65% every 10 days
So, b=0.0065 when h=10*24=240
now, we can plug values
[tex]P(t)=2100(1-0.0065)^{\frac{t}{240} }[/tex]
now, we can plug t=186
and we get
[tex]P(186)=2100(1-0.0065)^{\frac{186}{240} }[/tex]
[tex]=2089.413[/tex]
Answer:
Q(186) = 2089.463
Step-by-step explanation:
Formula for decaying exponentially:
Q(t) = Q_0 e^{-rt}
where, Q(t)= quantity at time t
Q_0 = initial quantity value (2100)
t = time (186 hours)
r = rate of decaying (0.65)
r = 0.65% = 10 days
1 day = [tex]\frac{0.0065}{10}[/tex]
1 hour = [tex]\frac{0.0065}{240}[/tex]
186 hours = [tex]\frac{0.0065*186}{240}[/tex]
rt = 0.00503
Q(186) = 2100*e^{-0.00503}
= 2089.46
Find the illegal values of b in the fraction
Answer:
[tex]b=4\text { or }b=-2[/tex]
Step-by-step explanation:
We have been given a rational expression: [tex]\frac{2b^2+3b-10}{b^2-2b-8}[/tex] and we are asked to find the illegal values of b.
Illegal values of b will be those values, which will make our denominator 0.
To solve for illegal or excluded values of b, let us set our denominator equal to 0.
[tex]b^2-2b-8=0[/tex]
We will factor out our equation by splitting the middle term.
[tex]b^2-4b+2b-8=0[/tex]
[tex]b(b-4)+2(b-4)=0[/tex]
[tex](b-4)(b+2)=0[/tex]
[tex]b-4=0\text { or }b+2=0[/tex]
[tex]b=4\text { or }b=-2[/tex]
Therefore, [tex]b=4\text { or }b=-2[/tex] are illegal values of b in the given fraction.
Please help!Which expression is equal to ....
Notice how the x-2 on the numerator and denominator cancel out, as well as the x+1. You are left with 8(x+2)/4 which is 2(x+2) which results in your answer, B, or 2x+4.
Suppose you toss a coin 100 times and get 69 heads and 31 tails. Based on these results, what is the probability that the next flip results in a head ?
The probability that the next flip results in a head is approximately __ ?
Answer:
69% or 69/100
Step-by-step explanation:
It's experimental odds based off of experience.
The probability of getting a head on the next flip is 69%.
Explanation:In order to determine the probability of getting a head on the next flip, we must first analyze the given data. The number of heads obtained in the first 100 flips is 69, while the number of tails is 31. Based on this information, we can calculate the proportion of heads to the total number of flips. The probability of getting a head on the next toss is therefore 69/100 = 0.69 or 69%.
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!!!!Which ordered pair in the form of (x, y) are solutions to the equation 7x - 5y =28
Answer:
(-6,-14)
Step-by-step explanation:
The length of a rectangle is 8 cm longer than its width . Its perimeter is more than 28cm . If W represents the width of the rectangle what expression represents the length in terms of the width
Answer:
W + 8
Step-by-step explanation:
Given:
The length of the rectangle is 8 cm longer than its width.
Let's take "W" be the width.
Length = W + 8
The expression "w + 8" represents the length of the rectangle.
Thank you.
Answer:
L=W+8
Step-by-step explanation:
This means that whatever number of centimeters the width is, you will always add 8 centimeters in order to reach the size of the length. In order to calculate the perimeter of the rectangle you have to add all its four sides and the final formula would be as follows:
W+W+L+L=P, where W is Width and L, is Length (W+8).
In other words, you can calculate as shown below:
W+W+(W+8)+(w+8)=P
HELP! Convert this identity to one using sine terms only !
1-2 cos^2 r=
A. -1-sin^2r
B. 2sin^2r-1
C. 1-2sin^2t
Please explain!
Answer:
option B is correct.
[tex]2\sin^2r - 1[/tex]
Step-by-step explanation:
Given the expression: [tex]1-2\cos^2r[/tex] ......[1]
Using trigonometric identities:
[tex]\sin^2r+ \cos^2r = 1[/tex]
We can rearrange this as;
[tex]\cos^2r = 1-\sin^2r[/tex] ......[2]
Substitute equation [2] into [1] we get;
[tex]1-2(1-\sin^2r)[/tex]
Using distributive property: [tex]a\cdot (b+c) = a \cdot b + a\cdot c[/tex]
[tex]1- 2 +2sin^2r[/tex]
or
[tex]-1+2\sin^2r[/tex]
therefore, the given expression in terms of sine terms is; [tex]2\sin^2r-1[/tex]
HELP FAST! 15 POINTS! PLEASE HELP!
which table shows a proportional relationship between x and y ?
Answer:
Step-by-step explanation:
Basically, in each option, you have to find the relationship between x and y (for one pair). Like in option #1 - how do you get 1.5 from 3? divide it by 2. Now you apply it for all numbers. It the outcome the same? No. 7 ÷ 2 ≠ 3.
You do the same process for all, until you are left with the last one. y = 50x
The last option is the answer.
use the coordinates of the labeled points to find a point-slope equation of the line. (3,-4)
Answer:
slope=-3
y=-3x+5
Step-by-step explanation:
use two given points (3,-4)(0,5)
5- -4= 9
0-3=-3
9/-3=-3
Answer: [tex]y+4=-3(x-3)[/tex]
Step-by-step explanation:
The point-slope equation of a straight line is:
[tex]y-y_{1}=m(x-x_{1} )[/tex]
where m is the slope and [tex](x_{1}, y_{1} )[/tex] are the coordinates of a point in the line.
So, to find the equation, the firs step is to find the slope. We can see in the graphic that the line intercepts the y axis at the point (0, 5), so we're going to use that and the other given point to find the slope:
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}} =\frac{-4-5}{3-0} =\frac{-9}{3}=-3[/tex]
Then, you simply substitute the slope and the coordinates of the point and you get the point-slope equation:
[tex]y-(-4)=-3(x-3)\\y+4=-3(x-3)[/tex]
A company has a monthly profit, or gain, of 6400. The next month they have a loss of 4,700.What expression would you use to find the difference in profit between the two months ?
Answer:
P₂ - P₁ = -11 100
Step-by-step explanation:
The profit for month 1 was P₁.
The profit for month 2 was P₂.
The difference in profit was
Diff. = P₂ - P₁
P₁ = 6400; P₂ = -4700
Diff. = - 4700 - 6400
Diff. = -11 100