A ratio of two numbers a/b, where b is no zero
[tex]{ \large{ \red{{\green{✮}} \: \: \sf{A \: \: number \: \: in \: \: the \: \: form \: \: of \: \:{\pink{ \frac{a}{b} \: \: where \: \: b≠0 }}\: \:{\orange{ is \: \: called \: \: a }}\: \: { \blue{ \underline{ \underline{ \tt{Rational \: \: Number}.}}}}}}}}[/tex]
Use the fact that
5.7 X 4.3 = 24.51
to work out
57 X 4.3
Answer:
57 x 457 x 4.3 = 10 x (5.7 x 4.3) = 10 x 24.51 = 245.1
Step-by-step explanation:
If we look closely at the two equations you will see the following...
57 x 4.3 = 10 x (5.7 x 4.3)
(Since we know what 5.7 x 4.3 equals to we just substitute the value of 24.51 and get...)
57 x 4.3 = 10 x 24.51
57 x 4.3 = 245.1
A line passes through the point (10,-8) and has a slope of -1/2. Write an equation in slope-intercept form for this line
The difference between x and 2 is less than 9
Answer:
difference between x and 2
Step-by-step explanation:
x-2< 9
x< 11
A horse can run at a top speed of 18 1/5 miles in 1/3 hour. What is the unit rate of the top running speed of a horse in miles per hour?
Answer:
54.6
Step-by-step explanation:
(18⅕ miles)/(⅓ hour) = ((18⅕)×3 miles)/hour = 54.6 miles per hour
The unit rate of the top running speed of a horse in miles per hour is 54.6 miles per hour.
What is the unit rate?There is an independent quantity, and a quantity that depends on it (dependent quantity). When independent quantity moves by a unit measurement (single unit increment), the increment in dependent quantity is called the rate of increment of dependent quantity per unit increment in independent quantity.
Speed can be calculated as the ratio of the distance traveled to the time taken by the object.
We have been given that horses can run at a top speed of 18⅕ miles in 1/3 hour.
Therefore, Distance = 18⅕ miles
Speed = 18⅕ miles in 1/3 hour.
Thus, we get;
Unit rate= (18⅕ miles) / (⅓ hour)
Unit rate = ((18⅕)×3 miles)/hour
Unit rate = 54.6 miles per hour
Therefore, the unit rate of the top running speed of a horse in miles per hour is 54.6 miles per hour.
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if y varies jointly as the square of x and the cube of z and inversely as the square root of w. When x = 2, z = 2, and w = 64, then y = 12. Find y when x = 1, z = 3, and w = 4.
Answer:
40.5
Step-by-step explanation:
if y varies jointly as the square of x and the cube of z and inversely as the square root of w, this is expressed as;
y ∝ x²z³/√w
y = kx²z³/√w
If x = 2, z = 2, y = 12 and w = 64
Substitute;
12 = k (2)²(2)³/√64
12 = 32k/8
12 = 4k
k = 12/4
k = 3
To get y when x = 1, z = 3, and w = 4.
y = 3 (1)²(3)³/√4
y = (3*27)/2
y = 81/2
y = 40.5
Hence the value of y is 40.5
Thirty percent of all the
drinks sold at the
concession stand were soda.
If 600 drinks were sold,
then how many drinks of
soda were sold?
Answer:
180 of the drinks sold were soda
Step-by-step explanation:
if we divide 600 by 0.30, which is 30%, we would get 180, so your answer would be 180.
Elizabeth has $10, $5, and $1 bills worth $101. she has five more five dollar bills than ten dollar bills and 4 times more 1 dollar bills than 10 dollar bills. How many of each kind of bills does elizabeth have?
Answer:
Let F = The number of $5 bills and T = the number of $10 bills. She has 15 bills total, so:
F+T = 15
T = 15-F
She has $120 total:
$120 = ($5)*F + ($10)*T
$120 = $5*F + ($10)*(15-F) [Substitute 15-F in place of T]
120 = 5F + 150 - 10F
-30 = -5F
6 = F
Check:
T= 15-F = 15=6 = 9
$120 = ($5)*6 + ($10)*9
$120 = $30 + $90
$120 = $120
Elizabeth had 4 of $10 bills, 9 of $5 bills and 16 of $1 bill.
EquationLet x represent the number of $10 bill, y represent the number of $5 bill and z represent the number of $1 bill. Hence:
10x + 5y + z = 101 (1)
Also:
y = x + 5 (2)
And:
z = 4x (3)
From equation 1, 2 and 3:
x = 4, y = 9, z = 16
Elizabeth had 4 of $10 bills, 9 of $5 bills and 16 of $1 bill.
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3(x-4)= 2(x + 5)
Find the number
Answer:
x=22
Step-by-step explanation:
Reorder the terms:
3(-4 + x) = 2(x + 5)
(-4 * 3 + x * 3) = 2(x + 5)
(-12 + 3x) = 2(x + 5)
Reorder the terms:
-12 + 3x = 2(5 + x)
-12 + 3x = (5 * 2 + x * 2)
-12 + 3x = (10 + 2x)
Solving
-12 + 3x = 10 + 2x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-2x' to each side of the equation.
-12 + 3x + -2x = 10 + 2x + -2x
Combine like terms: 3x + -2x = 1x
-12 + 1x = 10 + 2x + -2x
Combine like terms: 2x + -2x = 0
-12 + 1x = 10 + 0
-12 + 1x = 10
Add '12' to each side of the equation.
-12 + 12 + 1x = 10 + 12
Combine like terms: -12 + 12 = 0
0 + 1x = 10 + 12
1x = 10 + 12
Combine like terms: 10 + 12 = 22
1x = 22
Divide each side by '1'.
x = 22
Simplifying
x = 22
In the diagram, ∠XWY congruent to ∠ZWY. Find XY.
Answer:
10
Step-by-step explanation:
Let XY = a
Since,
XY + YZ = XZ
a + YZ = 24
YZ = 24 - a
By angle bisector property:
[tex]\frac{WX}{WZ} = \frac{XY}{YZ} \\ \\ \frac{15}{21} = \frac{a}{24 - a} \\ \\ \frac{5}{7} = \frac{a}{24 - a} \\ \\ 5(24 - a) = 7a \\ \\ 120 - 5a = 7a \\ \\ 120 = 7a + 5a \\ \\ 120 = 12a \\ \\ a = \frac{120}{12} \\ \\ a = 10 \\ \\ \implies \: XY = 10[/tex]
Ashlyn and her friends are making gingerbread houses. They need to divide 28 packages of gumdrops between 7 friends. There are 25 gumdrops in each package. How many gumdrops will each friend get?
Answer:
100 gumdrops per person
Step-by-step explanation:
We know that there are 28 packages and each one has 25. So just multiply 28 by 25 and you get 700 gumdrops in total. Finally because there are seven friends in total you divide 700 by 7 and get 100 per person.
F(x)=+6
Can you please brake this down for me step by step thank you
Answer:
below in explanation
Step-by-step explanation:
This basically means that for any value of x, the answer will always be 6
Answer And Step-by-step explanation:
F(x) = 6
^^ the domain of a constant function is the set of all real numbers.
so therefore; the answer is all real numbers
Plz help!!!!!!!!!!!!
Answer:
47.5 y²
Step-by-step explanation:
The formula for finding the area of a circle: πr²
The radius (r): 5.5
Square (multiply by itself) 5.5.
5.5² = 30.25
Multiply by pi (3.14).
94.985
This figure is a semicircle, therefore, divide the area by 2.
47.4925
Round to the nearest tenth.
47.5
The area of this figure is 47.5 y².
A circle P is circumscribed about a regular hexagon ABCDEF
If segment AD is drawn, ADEF is a
Select one:
O a. rhombus
O b. rectangle
O c. trapezoid
O d. square
Answer:
C. Trapezoid
Step-by-step explanation:
A hexagon is a polygon with six sides, thus and six interior angles ABCDEF. After the segment AD (which is the diameter of the circle P) has been drawn, it divides the hexagon into two halves. With each half forming the shape of a trapezoid, so that ADEF is a trapezoid.
Thus, the appropriate option is C, trapezoid.
Let f(x) = - 4x+2 and g(x) = x2 + 2.
Find (f+g)(x).
Answer:
[tex]x^{2}[/tex]-4x+4
Step-by-step explanation:
Solve the equation. Select all equivalent forms of the answer.
X-8= 5x + 3
[mark all correct answers]
a. -2.75
b. -0.36
c. -11
4
d. 1
e.
SUMO Some people believe that the N(555, 101)lbs distribution is not the correct model for sumo wrestlers’ weights. Their opinion is that the N(326, 80)lbs distribution is a better model. Manny Yarbrough, a former American sumo wrestling champion, weighed roughly 700 lbs.
If we use the N(555, 101)lbs model, would Manny’s weight be considered typical or unusually high?
i. There is a certain number that you would calculate and then use to answer the above question. Which of the following options is it?
a. (700-555)/sqrt(101) = 14.43
b. (555-700)/sqrt(101) = -14.43
c. 700/sqrt(101) = 69.65
d. (555-700)/101 = -1.44
e. (700-555)/101 = 1.44
f. 700-(3*101) = 397
g. 555-(3*101) = 252
Answer:
The answer is "Option e"
Step-by-step explanation:
use formula:
[tex]N(\mu\ , \ \sigma)= N(555,101)\\\\ \frac{N}{\mu}= 326\\\\\sigma=80\\\\\text{manny has weight}=700 \ lbs\\\\\to z-score= \frac{x-\mu}{\sigma}[/tex]
[tex]=\frac{(700-555)}{101} \\\\ = \frac{(145)}{101} \\\\ = 1.44[/tex]
to find the volume of something u can
Answer:
multiply length x width x height.
l x w x h
Mark practice the piano for 2/3 for an hour for 6 hours every week. How many hours does he practice each week
Answer:
9
Step-by-step explanation:
6 divided by 2/3 = 6 x 3/2 = 18/2 = 9
hope this helped!
Answer:
2/2
Step-by-step explanation:
Compare the wins-to-losses ratios for the teams.
Team Records
Team
Wins
Losses
Cougars
12
10
Bobcats
20
10
Bulldogs
8
5
Tigers
3
5
Which team has the greatest ratio of wins-to-losses?
Cougars
Bobcats
Bulldogs
Tigers
Answer:
Bobcats (i am assuming you need the team with the higest ratio of wins to losses)
Step-by-step explanation:
As a decimal cougars is 1.2 Bulldogs is 1.6 tgers is 0.6 and the largest is bobcats which os 2.0 so the answer is bobcats.
Answer:
B
Step-by-step explanation:
1/3 divided by 4 3/4
Answer:
0.07017543859
Step-by-step explanation:
I hope this helps have a nice day!
Arrange the following numbers in ascending order. (a) 5812214,
Answer:
1, 1, 2, 2, 4, 5, 8
Step-by-step explanation:
Hope this helps :)
Maybe brainliest?
Find the x- and y-intercepts of the graph of the equation.
x - 2y = 2
What is x in x - (-11) = -20
x is -31 because you had to add -11 and -20
give an example of two principal amounts and two periods of time for which the simple interest turned at 2.42 percent would be equal
PLEASE HELP, BRAINLIEST FOR THE CORRECT ANSWER
Answer:Case 1: Principal: 10,000; Period: 1 year Case 2: Principal: 1,000; Period: 10 years Case 3: Principal: 5,000; Period: 2 years Case 4: Principal: 2,500; Period: 4 years Simple Interest is a product of period, principal and interest rate, for a given interest rate, the interest earned would be equal if the product of principals and period is same for any number of cases. In our examples, we see that the product of principal and period comes out to be 10,000 in each case.
Step-by-step explanation:
find the tenth term in each sequence -14, -6, -2, 0, 1
Answer:
Step-by-step explanation:
Question 1 of 6
Use the guess and check method to solve this problem.
Blue cassettes hold 45 minutes of music. Green cassettes hold 55 minutes
of music. If Niko has 14 cassettes containing 710 minutes of music, how
many are blue, and how many are green?
O
A. 6 blue cassettes and 8 green cassettes
B. 3 blue cassettes and 11 green cassettes
O O O
C. 5 blue cassettes and 9 green cassettes
O D. 4 blue cassettes and 10 green cassettes
Loo
Answer:
A
Step-by-step explanation:
6 blue cassettes × 45 min = 270 min
8 green cassettes × 55 min = 440 min
270 min + 440 min = 710 min
<) Madison is organizing a 10K race. She is ordering cases of bottled water for the runners.
Each case contains 20 bottles of water. Madison wants to know the number of bottles, b,
she will receive based on the number of cases she orders, c.
) The variable b is the
dependent
variable.
The variable c is the
independent
variable.
) Write an equation that gives the total number of bottles, b, when Madison orders c cases.
+
=)
C
b
20
Answer:
b= 20 • c
b is equalled to how many bottles, which c is equalled to how many cases, since there is no number for how many cases then is just the variable "c".
The equation representing the number of bottles is c = 20b
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
For example, 3x - 5 = 16 is an equation.
Given that, Madison ordered c cases of the bottle with each case having 20 bottles,
So, for c cases she will have 20b bottles.
The equation is :-
c = 20b
Here,
c is dependent variable
b is independent variable
Hence, the equation representing the number of bottles is c = 20b
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— 3х + Зу = - 24
how do i convert to slope intercept form
Answer:
y = x - 8
Step-by-step explanation:
Slope intercept form: y = mx + b, where b is the y-intercept.
Solve the given equation for y and then compare the result with this y = mx + b:
3y = 3x - 24
Dividing all three terms by 3 yields:
y = x - 8 (answer). The slope is 1 and the y-intercept is -8.
What's slope Line
pass through( 14, 4)( 21, 6