1.
The scale factor would be:
[tex]3\colon5[/tex]2.
Divide each original dimension by 4 and then multiply by 3, as following:
[tex]\begin{gathered} \frac{8ft}{4}\cdot3=6ft \\ \\ \frac{4ft}{4}\cdot3=3ft \end{gathered}[/tex]The smaller garden has a length of 6 ft and a widht of 3 ft
Find the volume of the top of the prism, volume of the bottom prism, and total volume of figure.
Volume of the top of the prism: 460 cm^3
Volume of the bottom of the prism: 1 768 cm^3
Total volume of the figure: 2 228 cm^3
Explanation:
Volume of the top of the prism:
. Since it is a prism from trapezoid
. . Volume = Area of the trapezium base * heights between trapezium ends
[tex]\begin{gathered} Area\text{ of a trapezium base}=\frac{top\text{ base+bottom base}}{2}*height \\ ...\text{ =}\frac{6+17}{2}*(22-17) \\ ...=\frac{23}{2}*5 \\ Area\text{ = 57.5 cm}^2 \end{gathered}[/tex][tex]Volume=57.5*8=460\text{ }cm^3[/tex]Volume of the bottom prism:
. Since the price has a rectangular base:
Volume = Area of one base * height between reactangular bases
Area of one base :
[tex]17*13=221\text{ }cm^2[/tex]Volume:
[tex]221*8=1\text{ }768\text{ }cm^3[/tex]Total volume of the figure:
Volume of the top + Volume of the bottom = Total volume
[tex]221+1\text{ }768=2\text{ }228\text{ }cm^3[/tex]NB:
To find any volume of a given prism, start with finding the area of one base, then multiply that area by the height (in other words the sides that link the two bases)
How do we determine the strength of a correlation?
OA. The more closely two variables follow the general trend, the stronger the correlation (which may be positive or negative).
GB. Negative correlation is stronger than no correlation. Positive correlation is stronger than negative correlation.
OC. The more closely two variables follow the general trend, the weaker the correlation (which may be positive or negative).
OD. No correlation is stronger than negative correlation. Positive correlation is stronger than no correlation
We can determine the strength of a correlation by A. The more closely two variables follow the general trend, the stronger the correlation (which may be positive or negative).
What is correlation?Correlation is a statistical term that reflects how closely two or more variables are related to one another. Correlation is measured on a scale of -1 to +1, with 0 indicating a negative correlation and > 0 indicating a positive correlation. A value of 0 implies that there is no association.
A positive correlation is a two-variable association in which both variables move in lockstep. A positive correlation exists when one variable declines while the other increases, or when one variable increases while the other falls. The number one represents a perfect positive association.
If there is an increase or decrease in one variable results in increase or decrease in the other then there is correlation. If the value of correlation is close to either extremities (+1 or +1) then there is strong correlation.
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Meghan measures the heights and arm spans of the girls on her basketball team. She plots the data and makes a scatterplot comparing heights and arm spans, in inches. Meghan finds that the trend line that best fits her results has the equation y=x+2 . if a girl on her team is 64 inches tall, What should Meggan expect her span to be?
EXPLANATION
Let's see the facts:
The equation is given by the following expression y= x + 2
---> 64 inches tall
As we can see in the graph of arm span versus height, and with the given data the arm span should be:
arm span = y = 64 + 2 = 66 inches
So, the answer is 66 inches. [OPTION C]
Find the slope of the line that goes through the given points.
(-3,-2) and (– 15,13)
Answer:
Answer:
Slope m= [tex]-\frac{5}{4}[/tex]
As a decimal:
m = -1.25
Step-by-step explanation:
[tex]m=\frac{Rise}{Run} =\frac{y}{x} \\m=\frac{y2-y1}{x2-x1} \\m=\frac{13--2}{-15--3} \\m=\frac{15}{-12} \\m=-\frac{5}{4}[/tex]
in the figure below, when the sun angle of elevation is 50°, the tree casts a shadow 80 feet long which can be used to find the height of the tree?
We can use the tangent of 50º. The height is approximately 95.34 ft
1) We can trace a right triangle over that mark and calculate that height, using a trigonometric ratio.
2) As we have the adjacent leg to that 50º angle and the opposite leg, we can use the tangent of 50º to find that height out.
[tex]\begin{gathered} \tan (50)=\frac{x}{80} \\ x=80\cdot\tan (50) \\ x\approx\text{ 95.34} \end{gathered}[/tex]3) Hence the answer is
We can use the tangent of 50º. The height is approximately 95.34 ft
HELP PLEASE!!!!!!!!!!! ILL MARK BRAINLIEST
Answer:
skill issue
Step-by-step explanation:
skill issue
Identify the slope and y-intercept of the line y=−2x−1.
Given the equation of the line:
[tex]y=-2x-1[/tex]The given equation as the slope-intercept form: y = m * x + b
where m is the slope and b is the y-intercept
the y-intercept is the value of y when x = 0
By comparing the given equation with the slope-intercept form
So,
The slope = m = -2
The y-intercept = b = -1
the point of y-intercept = ( 0, -1 )
9) Write an equation of a line that is steeper than y- 6x + 2
O GRAPHS AND FUNCTIONSDomain of a rational function: Excluded values
Recall that the domain of a rational function consists of all the real numbers x except those for which the denominator is 0.
The denominator of the given rational function is:
[tex]d(x)=x^2+11x-18.[/tex]Notice that:
[tex]\begin{gathered} x^2+11x+18=x^2+2x+9x+9*2 \\ =x(x+2)+9(x+2)=(x+9)(x+2). \end{gathered}[/tex]Therefore d(x)=0 at x=-9 and x=-2, then those values are not in the domain of g.
Answer:
[tex]x=-9,-2.[/tex]Find an expression equivalent to the one shown below.913 x 9-6OA. 79OB.919OC. 97OD. 9-78
Answer:
C. 9⁷
Explanation:
We will use the following property of the exponents:
[tex]x^a\times x^b=x^{a+b}[/tex]It means that when we have the same base, we can simplify the expression by adding the exponents. So, in this case, the equivalent expression is:
[tex]9^{13}\times9^{-6}=9^{13-6}=9^7[/tex]Therefore, the answer is C. 9⁷
A box is filled with shoe boxes. Each shoe box has a volume of 1 cubic foot. Six shoe boxes can fit in each layer and the height of the box is 4 feet. What is the volume of the box?
shoe box = 1 cubic foot = 1 * 1 * 1
1 Layer: 6 shoe boxes -> Layer lenght = 6 feet, layer depht = 1 foot
Box height = 4 feet
Box volume = 6*4*1 = 24 feet
Ali took 3 1/4 hours to clean the bathroom. Then he took 1/8 hours to clean the kitchen. How much total time did Ali take to clean the two rooms?Write your answer as a mixed number in the simplest form.
He took 3 1/4 hours to clean the bathroom and then he took 1/8 hours to clean the kitchen.
First, we can convert the mixed number 3 1/4 into a fraction:
3 1/4 = 3/1 + 1/4 = 13/4
Now, we can sum both times:
13/4 + 1/8 = ((13*8)+(4*1)) / (4*8) = (104 +4)/ 32 = 108/32 = 27/8
Finally, we need to convert the total of hours 27/8 as a mixed number:
If 27/8 = 3.375
We take the whole number and then convert the decimal remaining into a fraction:
3 - whole number
0.375* (1000/1000) = 3/8
Hence, the mixed number for the total time that Ali spent cleaning both rooms is 3 3/8
Which inequality is equivalent to this one?y-83-2O y-8+82-2-8O y 8+82-248o y 8+22-248o Y8+ 25-242
Given the inequality:
[tex]y-8\le-2[/tex]If we add 2 on both sides, the inequality remains the same and we get:
[tex]y-8+2\le-2+2[/tex]what would the annual rate of interest have to be? round to two decimal places.
To find:
The rate of interest.
Solution:
It is known that the rate of interest is given by:
[tex]r=n[(\frac{A}{P})^{\frac{1}{nt}}-1][/tex]Here. P = 60000, A = 61200, t = 2.5 and n = 12.
[tex]\begin{gathered} r=12[(\frac{61200}{60000})^{\frac{1}{12(2.5)}}-1] \\ r=0.00792366 \end{gathered}[/tex]Change into the percentage by multiplying by 100:
[tex]\begin{gathered} r=0.00792366 \\ r=0.79\% \end{gathered}[/tex]Thus, the answer is 0.79% per year.
i need help in this please
The isosceles right is given in the diagram below
We are to rotate clockwise about point B as the origin
Rotating ABC 180° Clockwisely, we have
Rotating ABC 270° clockwise about B, we have
We now combine the four triangles together in the diagram below
Please help ASAP!! 31 points and brainliest!
I really need help! Please show your work so I can understand how to get the answers too!
A relation is a function if it has only One y-value for each x-value. Functions f(2/3)=2/9 for f(x)=2x²-4x+2 and f(1/4)==-21/4 for f(x)=4x²+2x-6
What is a function?A relation is a function if it has only One y-value for each x-value.
The given function is
f(x)=2x²-4x+2
Put x=2/3
f(2/3)=2(2/3)²-4(2/3)+2
=2(4/9)-8/3+2
=8/9-8/3+2
=(8-24+18)/9
f(2/3)=2/9
Now f(x)=4x²+2x-6
Put x=1/4
f(1/4)=4(1/4)²+2(1/4)-6
=4/16+2/4-6
=1/4+1/2-6
= 1+2-24/4
f(1/4)==-21/4
Hence functions f(2/3)=2/9 for f(x)=2x²-4x+2 and f(1/4)==-21/4 for f(x)=4x²+2x-6
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I need help with this practice problem The subject is trigonometry
SOLUTION
The range of the function is given as:
[tex](-\infty,-9\rbrack\cup\lbrack5,\infty[/tex]The asymptote of the function is at points
[tex]x=0,x=2\pi[/tex]The function is shown in the graph below
Therefore, the equation of the session is
[tex]f(x)=7\csc (\frac{x}{2})-2[/tex]hi, can you please explain mistake made on one side the other side the correct work with the answer thanks
Notice that:
[tex]3x-3x\ne x,[/tex]therefore the mistake is the last step.
Now, all the work of the student is correct up to:
[tex]undefined[/tex]hi i need help here please help me i am in need of the helps
The area of the octagon shaped stop sign = areas of the 4 rectangles + 4 triangles + square = 478 in.².
How to Find the Area of a Triangle and the Area of a Rectangle?Area of rectangle = (length)(width).Area of triangle = 1/2(base)(height).Area of square = (side length)².If the octagon can be decomposed into 4 identical triangles, 4 identical rectangles, and a square, the following are the dimensions of each of the shapes given:
Height of the triangle = (24 - 10)/2 = 7 in.
Base of the triangle = 7 in.
Side length of the square = 10 in.
Length of rectangle = 10 in.
Width of rectangle = 7 in.
The area of the octagon shaped stop sign = 4(1/2 × base × height) + 4(length × width) + (side length)²
Substitute the values into the equation
The area of the octagon shaped stop sign = 4(1/2 × 7 × 7) + 4(10 × 7) + (10)²
The area of the octagon shaped stop sign = 478 in.².
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Jason predicted that 227 students would attend the school dance.
The actual number was 250. What is the percent error of Jason's prediction?
.
1. What is the difference between the predicted value and the
actual value?
2. Complete the equation:__=p • ___
3. Solve the equation for p.
(I already did number one I just need help with 2 and 3)
Question 2
[tex]23=p \cdot 250[/tex]
The difference is 23.The actual value is 250.Question 3
[tex]p=\frac{23}{250}=0.092[/tex]
concetta had a 2kg bag of flour. she used 180g of flour to make biscotti. how many kilograms of flour are left in the bag?
Answer
The amount of flour left in the bag = 1.82 kg
Explanation
Concetta had 2 kg of flour.
She uses 180 g of the flour to make biscotti.
We are then asked to calculate how much flour is left in kilograms.
Amount of flour left = (Initial Amount of flour) - (Amount of flour used)
Initial amount of flour = 2 kg
Amount of flour used = 180 g = 0.18 kg
Amount of flour left = (Initial Amount of flour) - (Amount of flour used)
Amount of flour left = 2 - 0.18 = 1.82 kg
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Classify the following conic section from its standard equation: 4y2 - 6x +16y - 21 = 0.My
it is a parabolla because only variable is quadratic and the other is linear.
Which of the following numbers are not natural numbers?Select one:a. 1,000,000b. 5,032c. 1/4d. 25
Natural numbers are those who you use to count elements, they are by definition positive integers.
C. is not an integer, so it is not a natural number
b. 5032, a. 1000000 and d.25 are positive integers. These are natural numbers.
Prove that if 3/5 x = 9 then x = -15
Given: 3/5 x = 9
Prove: x = -15
There is no proof because X ≠ -15 when 3/5 x = 9
What is multiplication?Multiplication is defined as one of the basic arithmetic operations that is used for the repeated addition of similar figures together.
From the given expression,
3/5x = 9
But X= -15
Substitute X = -15 into the given expression;
That is,
3/5 * -15 = 9
-45/5= 9
-9 = 9
Therefore, there is no proof that in the expression 3/5 x = 9, X ≠ -15 because the final answer is -9 and not ,9.
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The cost of a pair of skis to a store owner was $700, and she sold the pair of skis for $1020.Step 3 of 3: What was her percent of profit based on selling price? Follow the problem-solving process and round your answer to thenearest hundredth if necessary.
Answer:
Explanation:
• The ,cost price ,of the pair of skis = $700
,• The ,selling price ,of the pair of skis = $1020
To calculate the percentage of profit, use the formula below:
[tex]\text{Percent of Profit=}\frac{Selling\text{ Price-Cost Price}}{\text{Selling Price}}\times\frac{100}{1}[/tex]Substitute the given values:
[tex]\text{Percent of Profit=}\frac{1020\text{-7}00}{\text{7}00}\times\frac{100}{1}\text{=}\frac{320}{\text{7}00}\times\frac{100}{1}=45.71\%[/tex]The percentage profit is % (correct to the nearest hundredth).
.. Find the values indicated. For g = {(-1,0), (-3,3), (-5, 6), (-7,9), (-9, 12)} g(-3) = g(-9) = g(-7)=
Given:
g = {(-1,0), (-3,3), (-5, 6), (-7,9), (-9, 12)}
So,
To find g(-3), we need to find the term that contains -3 in the location of x of the order pair
So, g(-3) = 3
And by the same manner, we will find the others
So,
g(-9) = 12
g(-7) = 9
Solve the inequality: -1 <= x - 3 > 7
-1 ≤x-3>7
So:
-1≤x-3
x-3>7
Solve each
-1≤x-3
Add 3 to both sides:
-1+3≤x-3+3
2≤x
x-3>7
add 3 to both sides:
x-3+3>7+3
x>10
Solution:
2≤x or >10
Alicia borrow 15000 to buy a car she borrowed the money at 8% for 6 years how much will she have to pay the bank at the end of 6 years
Answer:
Explanation:
First, we identify the main components:
• Principal = $15,000
,• Rate = 8% =0.08
,• Time = 6 years
[tex]undefined[/tex]DATE IN OUT IN OUT HOURS TEMPORARY EMPLOYEE TIME CARD NAME: Eugene Mueller 8/8 7:00 4:10 8/9 6:50 11:00 DEPT Sales 8/10 8/11 12:00 4:35 Note: No overtime rate. 10:55 3:25 EMPLOYEE SIGNATURE RATE per hour: $8.50 TOTAL HOURS:
Operations in Scientific NotationWrite two numbers in scientificnotationFind their sum, difference, product& quotient
Solution:
Let the two numbers be
[tex]20\text{ and 10}[/tex]In scientific notation, the numbers are
[tex]\begin{gathered} 20=2\times10^1 \\ 10=1\times10^1 \end{gathered}[/tex]The sum of the numbers will be
[tex]=(2\times10^1)+(1\times10^1)=10^1(2+1)=10^1(3)=3\times10^1[/tex]Hence, the sum is
[tex]3\times10^1[/tex]The difference between the two numbers will be
[tex]=(2\times10^1)-(1\times10^1)=10^1(2-1)=10^1(1)=1\times10^1[/tex]Hence, the difference is
[tex]1\times10^1[/tex]The product of the numbers will be
[tex]=(2\times10^1)\cdot(1\times10^1)=(2\times1)(10^{1+1})=2(10^2)=2\times10^2[/tex]Hence, the product is
[tex]2\times10^2[/tex]The quotient of the numbers will be
[tex]=\frac{2\times10^1}{1\times10^1}=\frac{2}{1}\times(10^{1-1})=2(10^0)=2\times10^0[/tex]Hence, the quotient is
[tex]2\times10^0[/tex]