The bookstore is selling 4 books for $10 in a clearance sale. If Regina has $28 to spend, how many books can she purchase in the clearance sale?
In this problem
Applying proportion
we have
4/10=x/28
solve for x
x=(4/10)*28
x=11.2
therefore
answer is 11 booksI'm not entirely sure what I'm supposed to be doing
The intercept between both lines, represents the solution to the system compounded by the equations for both lines. It means (3,4) is the solution to both lines A and B.
If a car travels at a speed of 45 mi/h fort hours, then travels 65 mi/h for m hours, what does theexpression 45t +65m represent?The expression represents the (select)
total distance travelled by the car (option D)
Explanation:
When speed = 45mi/h
time = t hours
when speed = 65mi/h
time = m hours
45t +65m means 45mi/h × t + 65mi/h × m
The formula that relates the speed and the time is distance:
speed = distance/time
distance = speed × time
The distance for the first speed and time = 45mi/h × t hours = 45t
The distance for the second speed and time = 65mi/h × m hours = 65m
The sum of the two distance = distance covered by the car = 45t + 65m
Hence, we can say the expression 45t +65m represents the total distance travelled by the car (option D)
find the equation of line with points (3, 3) that passes through a slope of 2/3
hello
the standard equation of a straight line is given as y = mx + b
y = y-coordinate
x = x-coordinate
m = slope
b = intercept
the points given are (3, 3) and the slope = 2 / 3
y = mx + b
y = 3
x = 3
let's substitute in our values and solve for b
[tex]\begin{gathered} y=mx+b \\ 3=\frac{2}{3}(3)+b \\ 3=2+b \\ b=3-2 \\ b=1 \end{gathered}[/tex]since we have the value of the slope, we can simply write the equation from y = mx + b to y = 2/3x + 1
[tex]y=\frac{2}{3}x+1[/tex]this is the equation of the line.
but we can further simplify this by looking for the LCM of the denominators of the independent variables
[tex]\begin{gathered} y=\frac{2}{3}x+1 \\ y=\frac{2x+3}{3} \\ \text{cross multiply both sides} \\ 3y=2x+3 \end{gathered}[/tex]the equation can be rewritten as 3y = 2x + 3
Find the area of the triangle with base 15 cm and height 18 cm.
From the problem, we have a triangle with base of 15 cm and a height of 18 cm.
The area of the triangle is :
[tex]A=\frac{bh}{2}[/tex]where b = base and h = height.
Using the formula above, the area will be :
[tex]A=\frac{15(18)}{2}=135[/tex]The answer is 135 cm^2
Recommendations Skill plans Math Common Core Fifth grade > * P.7 Guess-and-check problems DAJ Kurt bought 28 stamps at the post office. The number of stamps in each book was 7 times as large as the number of books. How many stamps were in each book? stamps Submit
28/7 = 4
There were 7 stamps in each book
evaluate the following expression 2 * 1 + 2 * 24/4
using PEDMAS/ BODMAS
division is executed first followed by multiplication then addition
In a study of 200 students under 25 years old one-fifth have not yet learned to drive. What percentage can drive?
The amount of garbage, G produced by a city with population p is given by G = f ( p ) . G is measured in tons per week, and p is measured in thousands of people. The town of Tola has a population of 45,000 and produces 6 tons of garbage each week. Express this information in terms of the function f. f = 6 / 45 f ( 45 ) = 6 f ( 6 ) = 45
Solution:
Given that the amount of garbage G produced by a city with population p is expressed as
[tex]\begin{gathered} G=f(p) \\ where \\ G\text{ is measured in tons per week} \\ p\text{ is measured in thousands of people} \end{gathered}[/tex]If a town Tola has a population of 45,000 and produces 6 tons of garbage per week, this implies that we substitute these parameters into the above equation.
This gives
[tex]6=f(45)[/tex]Hence, in terms of function f, the information is expressed as
[tex]f(45)=6[/tex]The second option is the correct answer.
a. 20% of 60 is ____ d. 50% of 90 is b. 25% of _____ Is 6 e. 10% of _ is 7c. _____% of 100 is 14 f. 30% of 70 is _
20% of 60 is 12
25% of 24 is 6
14% of 100 is 14
50% of 90 is 45
10% of 70 is 7
30% of 70 is 21
a. 20% of 60 is 12 because 60x20/100 = 60x0.2 = 12
b. 25% of 24 is 6 because 6x100/25 = 24
c. 14% of 100 is 14 because 100x(14/100) = 14
d. 50% of 90 is 45 is 14 because 90x50/100 = 45
e. 10% of 70 is 7 because 7x100/10 = 70
f. 30% of 70 is 21 because 70x30/100 = 21
n% of m is (n x m)/100
For example: 20% of 60 is (20 x 60)/100 = 1200/100 = 12
Find quotient of 5,433 % 8
Find the quotient of 5,433 by 8.
8 | 5,433
Divide 54 by 8. The quotient is 6. 6x8 = 48. 54 - 48 = 6.
6
8 | 5433
-48
-------
63
63 by 8 is 7. 7x8 = 56. 63 - 56 = 7.
67
8 | 5433
-48
-------
63
-56
--------
73
73 by 8 is 9. 9x8 = 72. 73 - 72 = 1. The final step is:
679 <== Quotiet
8 | 5433
-48
-------
63
-56
--------
73
-72
-------------
1 <== Remainder
Please helpWrite 78 percent as fraction In simplest form
Step 1:
In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".
Step 2:
[tex]\begin{gathered} 78\text{ percent = }\frac{78}{100} \\ To\text{ write to the simplest fraction} \\ \text{Divide both the numerator and the denominator by 2} \\ \frac{78}{100}\text{ = }\frac{39}{50} \end{gathered}[/tex]Final answer
[tex]\frac{39}{50}[/tex]Art wants to calculate the diagonal distance across opposite corners of a rectangular parcel. The parcel is 161’ by 326’ . How long is the diagonal measurement?
Recall that the formula for the length of the diagonal of a rectangle is:
[tex]l=\sqrt[]{a^2+b^2}.[/tex]Where a, and b are the lengths of the sides of the rectangle.
Substituting a=161´, b=326´ in the above formula we get:
[tex]\begin{gathered} l=\sqrt[]{(161^{\prime})^2+(326^{\prime})^2}, \\ l=363.5890537^{\prime}\text{.} \end{gathered}[/tex]Answer: 363.5890537 ´.
use only commutative property of addition to rewrite the expression 619+59
Given:
Given the sum 619+59
Required: Another expression using commutative property and the simplified expression
Explanation:
The commutative property says that for any two real numbers,
[tex]a+b=b+a[/tex]So, the expression 619+59 can also be written as 59+619, using commutative property.
Now, find the sum.
So, the sum is 678.
Final Answer: Another expression of 619+59 is 59+619 and its sum is 678.
I am thinking of a number. It has two digits. When I reverse the digits and then add the new number to the original number I get 33. What is my number?
I am thinking of a number. It has two digits. When I reverse the digits and then add the new number to the original number I get 33. What is my number?
Let
the number xy
so
Reverse the digits yx
xy+yx=33
10x+10y=30 ------> equation 1
y+x=3 ----> equation 2
solve the system by graphing
the syste
please help me solve this step by step with wrriten explanation. context and words help me
1/4 -86.205/4.121121112....123253^2/5 [tex] \sqrt{ \frac{4}{9} } [/tex][tex] \sqrt{20} [/tex]-1/2[tex]\pi[/tex].1223334444....16666....[tex] ^{3} \sqrt{27} [/tex][tex] - \sqrt{25} [/tex][tex]3\pi[/tex][tex] \binom{12}{4} [/tex][tex] \sqrt{17} [/tex]Okay finally tell me which numbers go in :Natural NumbersWhole Numbers Integers Rational Numbers Irrational Numbers
Natural numbers are the non-negative integers
So we will put inside its circle all the positive integers and zero
Let us find them using the 1st picture
there are 0 and square root 36 because its value is 6
Whole numbers are positive numbers only
So we can put 0 in a natural circle and 6 in the whole part and 12/4 because it equals 3
Integers are positive and negative whole numbers
We have -8 and - square root 25 because it equals -5
So put -8 and - square root 25 in the integer circle
Rational numbers are all numbers can but in the form of the fraction
So we will choose the number with decimal or fraction
6.2, -1/2, 2.21 on the rational part
The rest of the numbers are irrational numbers
Put them in the part of irrational numbers
5Graph the solution to – 2 < 2d – 2 < 6 -
Answer:
Explanation:
Here, we want to solve and graph the compound inequaqlity
We start by solving the sides, one at a time
[tex]\begin{gathered} -2\text{ < 2d-2} \\ -2+2\text{ < 2d} \\ 0\text{ < 2d} \\ 0\text{ < d} \end{gathered}[/tex]For the second part, we have:
[tex]\begin{gathered} 2d-2\text{ }\leq\text{ 6} \\ 2d\leq\text{ 6 + 2} \\ 2d\leq\text{ 8} \\ d\text{ }\leq\frac{8}{2} \\ d\leq\text{ 4} \end{gathered}[/tex]Now, let us write the solution in compound from:
[tex]0\text{ < d }\leq\text{ 4}[/tex]Finally, we proceed to plot the graph as follows:
how many people are :9 or younger ?At most 60 years old ?40 to 59 ?
Given the table represents the ages of people :
We need to find the following:
1. how many people are : 9 or younger ?
As shown in the table : the ages 0 - 9 has a frequency of 8
So, the answer is : 8 people
2. How many people at most 60 years old ?
From the table : the age 60 - 69 the frequency is 10
But there is no information to specify the age 60
The answer is : NEI
3. How many people are : 40 to 59 ?
From the table :
the age 40-49 has a frequency = 9
the age 50-59 has a frequency = 6
So, the answer is 9 + 6 = 15 people
Frank's rectangular box of toys has a perimeter of 30 inches. The length is twice as long as the width. Which of the following expressions could be a major step in finding the length? A. Length times Width equals AreaB. 2 times Width plus 2 times Width plus Width plus Width equals 30C. Perimeter equals Width plus Width plus Width plus WidthD. 2 times Length equals Width
From the given problem,
length is twice as long as the width
length = 2 x width
Note that the perimeter is :
[tex]P=2W+2L[/tex]where W and L are the width and length respectively.
Since L = 2W
Perimeter will be :
[tex]\begin{gathered} P=2W+2(2W) \\ P=2W+4W \\ P=6W \end{gathered}[/tex]Perimeter is equal to 30 inches :
[tex]6W=30in[/tex]From the given choices, only B satisfies this condition.
2W + 2W + W + W = 30
6W = 30
Therefore, the answer is B.
A cylinder has a height of 44.5 inches and a radius of 22.8 inches. Which of the following measurements is closest to the lateral surface area of the cylinder in square inches? F 6,374.9 in.2 G 145,274.5 in.? H 3,185.8 in. ? J 2,029.2 in.2 2.
We have the following:
The formula for the lateral surface area of a cylinder is as follows
[tex]LSA=2\cdot\pi\cdot r\cdot h[/tex]replacing:
[tex]\begin{gathered} LSA=2\cdot3.14\cdot22.8\cdot44.5 \\ LSA=6371.7 \end{gathered}[/tex]Therefore the answer is F 6374.9 in ^ 2
BD is the perpendicular bisector of ac,ac=10and bc=7 find the length of ad and ab
Since, BD is the perpendicular bisector of AC. So, AD = 1/2(AC) = 5.
Since, BD is the perpendicular bisector of AC and BC is not equal to AC. So, triangle ABC is an isosceles triangle. Therefore, AB = BC = 7.
The population of people in a town increases by 100 each year. Which equation represents the situation? Let p represent the amount the population has increased and t represent the number of years.t = 100 + pp = 100 + tt = 100pp = 100t
From the problem, the population increases by 100 each year.
a constant increase of 100 means that the slope of a line is 100.
Slope is the same as constant increase or rate of increase.
The equation of the line with a slope is :
[tex]y=mx+b[/tex]where m is the slope and b is the initital population.
Since we dont have an initital population, b = 0.
The equation will be :
[tex]y=100x[/tex]It is stated also that P represents the population that has increased. So y will be p.
and t represent the number of years. So x will be t.
That will be :
[tex]p=100t[/tex]ANSWER :
The equation is p = 100t
please help me 60 points please show all work this is due in 15 minutes5x-(3x-6)=182(3x-4)=102x+7=5x+16x/3-8=-23x – 6 = -12x/-3=8
Find the volume of the rectangular prism O 8 cubic units O 4 cubic units 6 cubic units O 3 cubic units
Given data:
The given rectangular prism.
The volume of the given prism is,
[tex]\begin{gathered} V=6(\text{volume of a cube)} \\ =\text{ 6(1 cubic-units)} \\ =\text{ 6 cubic-unis} \end{gathered}[/tex]For the following exercises, determine the least possible degree of the polynomial function shown.
Solution
To determine the least possible degree of the polynomial function
The function has atmost n - intercepts in the horizontal
The graph turns 4 times in the above curve, hence n = 4
[tex]\begin{gathered} n+1 \\ n=\text{ number of turns} \\ 4+1=5 \end{gathered}[/tex]Therefore the least possible degree of the polynomial = 5
Hence it is a 5 possible polynomial function
I have no clue how to graph inequalities and find the solution
In the graph we can see two line y=2 and y=x.
Also, we know that there is a system of inequalities and the blue area in the graph represent the solutions for the system.
We can see that the blue area is above the line y=2, thats mean one inequality is:
[tex]y\ge2[/tex]So, any points that y-coordinate is greater than or equal than 2 satisfy the inequality.
Also we can see that the blue area is bellow the line y=x and the line is a dotted line, this last means the inequality do not take take value in the line. So, the second inequation is:
[tex]ySo, the points that satisfy the system of inequalities are above the line y=2 and bellow the line y=x and not touch the line y=x.You'll have to make a series of transformations to make this parabola fit the bridge. Describethem
The transformations are as follows:
- There is firstly a vertical reflection
- There is a vertex shift from (0,0) to the (-2, 3) position (approximate)
- There is also a horizontal compression of the parabola.
Which choice is equivalent to the quotient shown here when x > 0?A.2xB.2x2C.D.
Given
[tex]\sqrt{22x^6}\div \sqrt{11x^4}[/tex]Solution
[tex]\begin{gathered} \frac{\sqrt{22x^6}}{\sqrt{11x^4}}=\sqrt{\frac{22x^6}{11x^4}} \\ \\ =\sqrt{\frac{22x^6}{11x^4}} \\ \\ =\sqrt{2x^2} \\ \\ =x\sqrt{2} \end{gathered}[/tex]The final answerOption C[tex]x\sqrt{2}[/tex]Please help me with these 2 questions they are both solved problems that go together with one huge problem so please answer both thank you
1).
r = 11 in
The diameter is twice the radius, so:
d = 2*11 = 22 inches
2).
d = 18 inches
The radius is half the diameter, so:
r = 18/2 = 9 inches
write a ratio that is equivalent to the ratio: 9/12
the given ratio is
9/12
divide numerator and denominator by 3
[tex]\frac{\frac{9}{3}}{\frac{12}{3}}=\frac{3}{4}[/tex]so the equivalent ratio is 3/4