the area is simply the product of its width and length, so hmmm before doing so, let's change all the mixed fractions to improper fractions and then multiply.
[tex]\stackrel{mixed}{4\frac{1}{5}}\implies \cfrac{4\cdot 5+1}{5}\implies \stackrel{improper}{\cfrac{21}{5}} ~\hfill \stackrel{mixed}{4\frac{2}{7}} \implies \cfrac{4\cdot 7+2}{7} \implies \stackrel{improper}{\cfrac{30}{7}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{21}{5}\cdot \cfrac{30}{7}\implies \cfrac{21}{7}\cdot \cfrac{30}{5}\implies \cfrac{3}{1}\cdot \cfrac{6}{1}\implies \text{\LARGE 18}~in^2[/tex]
The area of the rectangle is 18 [tex]inch^{2}[/tex] and the perimeter is [tex]16\frac{34}{35}[/tex] inches.
We know that, Area of a rectangle = l * b
and Perimeter of a rectangle = 2(l + b)
Where, l = length of the rectangle
b = breadth of the rectangle
According to the question, l = [tex]4\frac{1}{5}[/tex] inch = [tex]\frac{21}{5}[/tex] inch
b = [tex]4\frac{2}{7}[/tex] inch = [tex]\frac{30}{7}[/tex] inch
Area of the given rectangle = l* b
= [tex]\frac{21}{5}[/tex] * [tex]\frac{30}{7}[/tex]
= 18 [tex]inch^{2}[/tex]
The perimeter of the given rectangle = 2(l + b)
= 2( [tex]\frac{21}{5}[/tex] + [tex]\frac{30}{7}[/tex])
= 2 ([tex]\frac{297}{35}[/tex])
= [tex]\frac{594}{35}[/tex]
= [tex]16\frac{34}{35}[/tex] inch
Hence, the area of the rectangle = 18 [tex]inch^{2}[/tex]
and the perimeter = [tex]16\frac{34}{35}[/tex] inch
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Ken has 7 baseballs. Each baseball weighs 0.3 pound. Ken wants to use this
model to find the total weight of
the baseballs. Each hundredths block in the
model represents 1 whole.
Use the drop-down menus to explain how Ken can use
the model to find the total
weight of the baseballs. Click the arrows to choose an answer from each menu.
TO represent the weight of
one baseball, 0.3 pound, Ken should shade 3
Choose...
To represent the weight of all of the baseballs, he should
shade this amount Choose…
times. The shaded part of the model will represent
the expression
Choose...
. The total weight
of the baseballs is
Choose...
pounds.
The shaded part of the model will represent the expression 0.3×7= 2.1 and the total weight of the baseball is 2.1 pounds.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
Ken has number of baseballs = 7 and each baseball have a weight is = 0.3 pounds
By unitary method;
If 1 ball = 0.3 pounds
Then, 7 baseball = 7×0.3 pounds
So, the weight of 7 baseballs = 2.1 pounds
We want to use the box to represent this data given in the following question .
Since, the weight of the baseball is in decimal points
Let 0.1 pounds be 1 Square box.
The weight of one base ball (0.3 pounds), ken should shade 3 Square box.
Since 1 pounds is 1 Square box.
The weight of all the seven base ball (2.1 pounds), he should shade this amount seven times.
Therefore, the shaded part of the model will represent the expression 0.3×7= 2.1 and the total weight of the baseball is 2.1 pounds.
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5
LESSON 15 QUIZ
Name:
Latoya's punch bowl holds 80 oz of punch. That is enough for exactly 16 servings.
Decide if each statement about number of servings is true or false.
Choose True or False for each statement.
a. There are 20 oz of punch for every 5 servings.
b. There is 1 oz of punch per serving.
c. There are 5 oz per serving of Latoya's punch.
d. There are 16 oz in every serving of Latoya's punch.
Answer: It would be C
Step-by-step explanation:
80/16= 5oz
Answer:
Step-by-step explanation:
e. x=1
1. 3 x+4=7 x-8
2. 2 x=7 x-5
3. 5 x-8=5 x+12
4. 8 x+4=-2 x-16
5. -3 x+5=-3 x+5
A line passes through the points (2, -2) and (8, 1).
Click “show your work” and provide work for calculating the slope and y-intercept. Then, write the equation for the line in slope-intercept form. Please write your answers on the lines provided on the whiteboard.
Answer:
Slope: 1/2Y-intercept: -3Equation: y = 1/2x -3Step-by-step explanation:
You want the slope, y-intercept, and equation for a line that passes through the points (2, -2) and (8, 1).
SlopeThe slope formula is used to find the slope:
m = (y2 -y1)/(x2 -x1)
m = (1 -(-2))/(8 -2) = 3/6 = 1/2
Y-interceptThe slope-intercept equation can be rearranged to give the y-intercept:
b = y - mx
b = 1 -(1/2)(8) = 1 -4 = -3 . . . . . . using (x, y) = (8, 1)
Slope-Intercept FormThe slope-intercept form equation is ...
y = mx +b . . . . . . where m is the slope, and b is the y-intercept
Using the found values, the equation is ...
y = 1/2x -3
SummarySlope: 1/2Y-intercept: -3Equation: y = 1/2x -3Melinda has three empty boxes and 12 textbooks, three of which are mathematics textbooks. One box will hold any three of her textbooks, one will hold any four of her textbooks, and one will hold any five of her textbooks. If Melinda packs her textbooks into these boxes in random order, the probability that all three mathematics textbooks end up in the same box can be written as m/n, where m and n are relatively prime positive integers. Find m+n.
The probability of all three mathematics textbooks ending up in the same box can be written as m/n, where m and n are relatively prime positive integers. Since m and n are positive integers, the sum of m and n is also a positive integer and is equal to 27.
There are 12 textbooks total, 3 of which are mathematics textbooks.
1 box will hold 3 textbooks, 1 box will hold 4 textbooks, and 1 box will hold 5 textbooks.
Therefore, there are 3! (6) ways for the mathematics textbooks to be divided among the boxes.
The probability that all three mathematics textbooks end up in the same box can be written as m/n, where m and n are relatively prime positive integers.
m+n
=6/1=6
Therefore,
m+n
=27.
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Play department store by 300 shirts for a total cost of $7200 and sells them for $30 each. Find the percent markup.
Answer: The store has a markup percentage of 200%.
Step-by-step explanation: Markup percentage = (selling price - cost price) / cost price x 100%
Markup percentage = (30 - 10) / 10 x 100% = 200%
The store has a markup percentage of 200%. This means that the store has increased the price of the shirts by 200% above the cost price to make a profit.
Answer:
the percent markup is 25%.
Step-by-step explanation:
To find the percent markup, we need to know the difference between the cost price (what the store paid for the shirts) and the selling price (what the store is selling them for), and then divide that difference by the cost price and multiply by 100 to get the percentage.
Cost price = $7200 / 300 = $24
Selling price = $30
Profit = $30 - $24 = $6
Markup = (Profit / Cost price) * 100 = (6/24) * 100 = 25%
So the percent markup is 25%.
Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then graph the equation.
y=9 when x=1.5
The equation of variation is y= (Simplify your answer.)
The direct variation equation that relates x to y is written as y = 6x
How to write the direct variation relationIf y is directly proportional x. this is written as
y α x
y = mx
where m is the constant of variation
The equation shows that m which the constant of variation is the unit rate. In this case the slope
Hence we can say that the constant of variation in a direct variation equation is equal to the unit rate
when y = 9 and t = 1.5 m s solved to be
9 = 1.5m
m = 9 / 1.5
m = 6
the equation of variation of y is written as y = 6x
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gunpowder contains 65% nitre 15% sulphur and rest of it is charcoal find the amount of nitre sulfur and charcoal in 8kg of gunpowder
A class of students studied in preparation for the regent's exam. Its average score was initially 65, but because the students studied, this average grew at a rate of 1.1% each day.
a.) Write a function that would represent the average of the class.
b.) What would the average of the class be after one week?
A) The function that represents the average of the class is;
y = 65(1.011)^(x)
B) The average of the class after one week will be expressed as;
y = 70.17
How to solve Geometric Progression?The general formula for the nth term of a exponential function is;
y = ab^(x)
where;
a is initial amount
b is growth factor
x is the amount of periods being considered
Now, we are told that the initial score for the exam was 65. Thus;
a = 65
The growth factor is 1.1% and this is; b = 1.011
Thus, the function that represents the average of the class is;
y = 65(1.011)^(x)
The average of the class after one week will be expressed as;
y = 65(1.011)^(7)
y = 70.17
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Which graph shows the solution to this system of linear inequalities?
y >2x+3
y<-2x-4
Answer:
Rigid motion.
Step-by-step explanation:
please this was my opinion
use the given graph of the function to find the x-values for which f is not differentiable.
Answer (separate by commas): x=
The values of x for which the function is non-differentiable are given as follows:
x = -5.x = -3.x = -1.x = 2.x = 4.How to obtain the interval in which the function is differentiable?The points on a graph that make the function non-differentiable are given as follows:
Turning points.Discontinuities.Inflection points.Hence the non-differentiable points of the function graphed are listed as follows:
x = -5. -> turning point.x = -3. -> turning point.x = -1. -> discontinuity.x = 2. -> turning point.x = 4. -> inflection point.More can be learned about differentiable functions at brainly.com/question/22817336
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Who wants BRAINLIEST and BIG POINTS. Help me out folks :)
Answer:
The first, the third and the fifth figure
Step-by-step explanation:
Volume = Length x width x height
First
3 x 2 x 4 = 24
Second
3 x 2 x 5 = 30
Third
2 x 2 x 4 = 16
Fourth
2 x 3 x 4 = 24
Fifth
2 x 2 x 6 = 24
Answer:
Read below
Step-by-step explanation:
The first prism has 24 unit cubes.
The second has 30
The third has 16
The fourth has 24
The fifth has 24
You have to find the area of the superior blocks and then multiplied for the number of cube units of height.
The first has 6 unit cube because (2 cubes long * 3 cubes widht)* (4 blocks of alture)
6*4 = 24.
The same way for other and then you have that the first, the fourth and fifth have 24 cube blocks each one.
Write the equation of a line in slope-intercept
form that has a slope of -8 and a y-intercept
of (0, 3).
Answer:
y = -8x + 3
Step-by-step explanation:
b = y intercept
m = slope
y = mx + b
b = 0,3
m = -8
so therefore
y = -8x + 3
9n + a - 8 (n = 1 and a = 2)
9n+a-8
=9*(1) + 2 -8
=9+2-8
=3
The simplification of the given expression, 9n+a-8 is 3
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3. The number of terms in the following expression after being simplified and the leading coefficient
3x²+6+7x-4x² +8-3x²
2 terms and leading coefficient 3
B. 6 terms and leading coefficient -3
A.
C. 3 terms and leading coefficient -4
D. 2 terms and leading coefficient 7
The number of terms in the expression after being simplified and the leading coefficient will be 3 terms and negative 4. Then the correct option is C.
What is simplification?The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ 3x² + 6 + 7x - 4x² + 8 - 3x²
Simplify the expression, then we have
⇒ 3x² + 6 + 7x - 4x² + 8 - 3x²
⇒ - 4x² + 7x + 14
The number of terms in the expression after being simplified and the leading coefficient will be 3 terms and negative 4. Then the correct option is C.
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I’ll give BRAINLIEST if correct
Answer:
x + 13 (First option)
Step-by-step explanation:
Given:
Perimeter = 9x + 6
First side = 5x
Second side = 3x - 7
Let the length of the third side be A
Third side = A
Perimeter = First side + Second side + Third side
9x + 6 = 5x + 3x - 7 + A
9x + 6 = 8x - 7 + A
A = 9x + 6 - 8x + 7
A = x + 13
a contracter purchases 7 dozen pair of padded work glovs for $103.32. he incorrectly calculates the unit price at $14.76 what error did th contractor make
Answer:
The contractor made an error in calculating the unit price of the padded work gloves.
Step-by-step explanation:
To find the unit price of an item, we need to divide the total cost of the item by the number of units purchased. In this case, the contractor purchased 7 dozen pair of padded work gloves, which is equal to 7 x 12 = 84 pair of gloves. Therefore, the unit price of the padded work gloves is $103.32 / 84 pair = $1.23 per pair.
The contractor incorrectly calculated the unit price as $14.76, which is an error of $14.76 - $1.23 = $13.53. This error occurred because the contractor did not correctly take into account the number of units purchased when calculating the unit price.
Hope this helps:)
if you have a fraction with an exponent do you distribute the exponent to the denominator and the numerator
Yes, you would distribute the exponent to both the denominator and numerator. For example, if you had an expression like (2/3)^4, you would distribute the exponent to end up with (2^4)/(3^4).
For example, if you have an expression like (2/3)^4, the exponent of 4 should be distributed to both the numerator and denominator, resulting in (2^4)/(3^4). This is equivalent to multiplying the numerator and denominator by the same amount, 4 times. This is the same as writing (2*2*2*2)/(3*3*3*3), or simply
16/81.
1. Start with the expression
(2/3)^4
2. Distribute the exponent of 4 to the numerator and denominator, resulting in
(2^4)/(3^4)
3. This is equivalent to multiplying the numerator and denominator by 4, so (2^4)/(3^4)
= (2*2*2*2)/(3*3*3*3)
4. Simplify the expression to 16/81
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Name 2 decimals whose sum is between 0.5 and 0.6
Answer:0.2 and 0.35 i think i am not all the way sure
Step-by-step explanation:
is -5
whole number and irrational number.
B
integer and rational number.
C
rational number only.
D
integer only.
Answer:
Step-by-step explanation: The answer is B because a rational number is all numbers in existence and an integer is only positive and negative numbers.
Work out the volume of this hemisphere.
Give your answer to 1 decimal place.
1
8 cm
The volume of the hemisphere to 1 decimal place is 268.1 cm^3.
What is volume?Volume is the measure of the amount of space an object occupies or the space something takes up. Volume is typically measured in cubic centimeters, milliliters, liters, gallons, and cubic feet. Volume can also be used to describe the loudness of a sound or the amount of something that is produced. Volume is an important concept in physics and chemistry, as it is related to the properties of matter and energy.
To work out the volume of a hemisphere we can use the formula V = (2/3πr^3). Therefore, in this case, the volume of the hemisphere is (2/3πx8^3) = 268.08 cm^3. Therefore, the volume of the hemisphere to 1 decimal place is 268.1 cm^3.
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Anyone help to solve ?
The value of t₀.₀₁ is 3.355. The value 3.355 is rounded to three decimal places.
What is the critical value?
A crucial value is the test statistic's value that establishes a confidence interval's upper and lower boundaries or the level of statistical significance for a given test.
Any member of the family of continuous probability distributions known as the Student's t-distribution in probability and statistics is used to estimate the mean of a normally distributed population when the sample size is small and the population's standard deviation is unknown.
Given the value of v is 8.
Need to find the value of t₀.₀₁ when v = 8.
The value of t₀.₀₁ according to t distribution table is 3.3550.
= 3.355 (nearest to three decimal places)
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given that y a 1/x^2 complete this tables of values
x 1 2 5 10
y 100
The table with the numeric values of the function y = a/x² is given by the image presented at the end of the answer.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The function for this problem is defined as follows:
y = a/x².
When x = 1, y = 100, hence the coefficient a is calculated as follows:
100 = a/1
a = 100.
Meaning that the function is defined as follows:
y = 100/x².
To find the numeric value at x = 2, we replace the lone instance of x by 2, as follows:
y = 100/2² = 100/4 = 25.
The numeric value at x = 5 is then found as follows:
y = 100/5² = 100/25 = 4.
The numeric value at x = 10 is then found as follows:
y = 100/10² = 100/100 = 1.
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If the point (-3, 8) lies on the graph of a power function with an even exponent, which of the following
points must also lie its graph?
O (8,-3)
O (3.8)
O (3,-8)
O (-3,-8)
If the point (-3, 8) lies on the graph of a power function with an even exponent, the following points must also lie its graph is (8, -3): Option A
What is a graph?You should understand that a graph is the representation of a function using the graph papers.
It is given that (-3,8) is on the graph of F(x).
x-coordinate = 8, y-coordinate = -2
Interchange the coordinates to find the point which lies on the inverse function F⁻¹(x).
x-coordinate = 8, y-coordinate = -3
Therefore It means (8,-3) must be on the graph of the inverse function F⁻¹(x).
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Kiara, Giovanni, and Ebony are triplets and always argue over who can answer basic math facts the fastest. After
completing a few different math fact activities, Kiara, Giovanni, and Ebony record their data, which is shown below.
Kiara: m = 5t, where t represents the time in seconds,
and m represents the number of math facts completed.
Giovanni:
Seconds
Math Facts
5
20
10
40
15
60
1. What is the math fact completion rate for each student?
2. Who would win the argument? How do you know?
Ebony:
Number of Math Facts
56286368
60
30
24
18
Number of Math Facts Per Second
12
6
0
0 1 2 3 4 5 6
Number of Seconds
7 8 9 10
1. The math fact completion rate for each student is:
Kiara: m = 5t, where t represents the time in seconds, and m represents the number of math facts completed. Therefore, Kiara's math fact completion rate is 5 math facts per second.
Giovanni: Giovanni's math fact completion rate is 4 math facts per second.
Ebony: Ebony's math fact completion rate is 12 math facts per second.
2. Ebony would win the argument, as she has the highest math fact completion rate.
find the probability of drawing a red card on the first draw, replacing it then drawing a black card on the second draw
Answer: [tex]\frac{Amount of red cards}{Total cards} *\frac{Amount of black cards}{Total cards}[/tex]
Step-by-step explanation:
You didn't give how many cards there were, but just plug the amounts of cards that you have to get your probability.
Answer: 3/52 probability.
Step-by-step explanation:
You have 6 out of 52 cards that will satisfy the first draw of a red face card (J, Q, K of hearts and diamonds).
In the second draw, you have 26 out of 52 cards (i.e, 1/2) that will be black.
Now, multiply the two answers together, and you have (6/52) times (1/2) = probability of 3 out of 52, or 3/52.
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What is the answer to −3z−z
Answer:
-4z
Step-by-step explanation:
-3z - 1z Combine like terms
-4z
168 visitors purchased no costume. 252 visitors purchased exactly one costume. 47 visitors purchased more than one costume. Based on these results, express the probability that the next person will purchase no costume as a percent to the nearest whole number.
The probability that the next person will purchase no costume as a percent to the nearest whole number is 36.4%
What is probability as a percentage?We should know that probability deals with the chance of occurrence of an event (E)
The given parameters that will help us to get the percentage is
168 visitors purchased no costume 252 visitors purchased exactly one costume47 visitors purchased more than one costumeTotal number of visitors is 168+252+47
Total number = 462
The probability is = 168/(168+252+47) * 100/1
This implies 168/462 * 100/1
= 13.4 percent
In conclusion, 13% of the visitors will purchase no costume as a percent to the nearest whole number.
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plus or minus the square root of 49x^4
Answer:
± 7x²
Step-by-step explanation:
using the property of radicals
• [tex]\sqrt{ab}[/tex] ⇔ [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex]
given
± [tex]\sqrt{49x^4}[/tex]
= ± ([tex]\sqrt{49}[/tex] × [tex]\sqrt{x^4}[/tex] )
= ± (7 × x² )
= ± 7x²
Which graph shows a correlation coefficient closest to -1 ?
The first graph (topmost graph) shows a correlation coefficient closest to -1.
What is the correlation coefficient?A correlation coefficient is a statistical indicator of how well changes in one variable's value predict changes in another. When two variables are positively linked, the value either rises or falls together.
The -1 correlation coefficient indicates a negative correlation.
Variable y (vertical axis) should decrease as variable x (horizontal axis) increases.
As a result, the graph's gradient is negative and slopes downhill as x rises.
Graph 2 is eliminated (positive correlation approximately 1)
Graph 4 is incorrect as well because there is no association at all. (Points are arbitrary and lack a consistent pattern or trend.)
A negative correlation may be shown in graphs 1 and 3.
On the other hand, graph 3's straight line cannot be precisely drawn because some points are off. (Off somewhat) This graph's correlation is unfavorably skewed but not exactly -1.
Therefore, the first graph's correlation coefficient is the closest to -1.
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