Answer:
5/48
Step-by-step explanation:
(5/8 - 1/2) x 5/6
(5/8 - 4/8) x 5/6
1/8 x 5/6
5/48
Answer:
[tex]\dfrac{5}{48}[/tex]
Step-by-step explanation:
[tex]\left(\dfrac{5}{8} - \dfrac{1}{2}\right) \times \dfrac{5}{6}[/tex]
First, represent 1/2 as 4/8.
[tex]\dfrac{1}{2} \times \dfrac{4}{4} = \dfrac{4}{8}[/tex]
[tex]\left(\dfrac{5}{8} - \dfrac{4}{8}\right) \times \dfrac{5}{6}[/tex]
Then, simplify the subtraction.
[tex]\dfrac{1}{8} \times \dfrac{5}{6}[/tex]
Finally, multiply the numerators and denominators of the resulting fractions.
[tex]\dfrac{1 \times 5}{8 \times 6}[/tex]
[tex]\dfrac{5}{48}[/tex]
Uniforms are sold in packages of 4. The skating rink's 182 employees will
each be given 3 uniforms. How many packages will the skating rink need
to order?
Answer:
137
Step-by-step explanation:
182 employees x 3 uniforms = 546 uniforms needed
546/4 = 136.5
You can't buy a partial package, so you have to buy 137 packages. You'll have 2 extra uniforms.
Answer: 136.5
Step-by-step explanation:
182 x 3 = 546
546/4 = 136.5
You will have 137 packages with 2 uniforms left over.
Find the antilog of (2.4771)
The value of the antilog of the number, 2.4771, specified to base 10 is about 299.99.
What is the logarithm of a number?The logarithm of a number x at a base b, is the power or exponent to which b is raised to obtain the value of x
Mathematically; [tex]log_bx = y[/tex]
Therefore; [tex]b^y = x[/tex]
Where;
x = The argument; The possible values are; x > 0
y = The exponent; The possible values are; -∞ < y < ∞
b = The base of the logarithm; The possible values are; b ≠ 1 and b > 0
The antilog of a number can be obtained as follows;
The value x is the antilogarithm of the value y to base b. Therefore, the antilog of y is x where y is the logarithm of x
The values of the base of the logarithm
The antilog of a value is found by using the inverse of the process used to find the log of a value
The formula for the antilogarithm is presented as follows;
log₁₀x = y
The antilog of y is; x= [tex]10^y[/tex]
Therefore, the antilog of 2.4771 to base 10 is [tex]10^{2.4771}[/tex] ≈ 299.99Learn more about the logarithm of a number here: https://brainly.com/question/28595929
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A scale drawing of a square has a side length of 5 centimeters. The drawing has a scale of 1 cm : 5 ft. Find the actual perimeter and area of the square.
area =729 feet square and perimeter = 108 feet
Given the side of a square is 9 cm.
The scale is given as :
1 cm = 3 feet Since 1 cm represents 3 feet.
Therefore, 9 cm will represent = 9 x 3 feet= 27 feet
So the side of the square is 27 feet.Therefore, its area = Side x side= 27 x 27 = 729 feet square
And the perimeter = 4 x side= 4 x 27= 108 feet
What is perimeter?In the conventional system of measurement, an inch is a unit of length. Either in or " can be used to represent length in inches. For instance, 16 in or 16" can be used to write 5 inches. In both the British imperial and American customary systems of measurement, the inch serves as a unit of length. It is equivalent to 1/12 of a foot or 1/36 of a yard. a unit of length that is equivalent to 1/12 foot, or 2.54 centimeters, in length. In the conventional system of measurement, an inch is a unit of length. Either in or " can be used to represent length in inches.To learn more about perimeter refer to:
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Gavin and his three friends want to share 1/3 of a cake equally. Gavin says that each friend will get 1/9 of the cake. Use the drop-down menus to explain whether or not Gavin is correct.
Gavin's calculation is incorrect, each one of the friends will get 1/12 of the cake.
Is Gavin correct?We know that Gavin and his three friends want to share 1/3 of a cake equally.
So they want to divide 1/3 of a cake between 4 people, then we need to solve the quotient:
(1/3 of a cake)/4 = (1/3*4) of a cake = 1/12 of a cake.
So each friend will get 1/12 of a cake.
Instead of that value, Gavin said that each friend would get 1/9 of the cake, so his calculation is incorrect.
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An international company has 26,700 employees in one country. If this represents 34.2% of the company's employees, how many employees does it have in total? Round your answer to the nearest whole number.
Answer:
the answer
Step-by-step explanation:
none lol :))))))
The table shows how much money Earl's grandmother gave him each birthday.
Age Birthday Money
5 15
8 24
10 30
16 ?
At this rate, how much money should Earl receive from his grandmother when he turns 16?
$36
$48
$51
$55
$48 is the amount Earl receive from his grandmother when he turns 16
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that table shows how much money Earl's grandmother gave him each birthday.
As it is a proportional relation then
y=kx
Now let us take any point from the table
30=k(10)
k=3
So now we have to find value of y when x is 16
y=3×16
y=48
Hence, $48 is the amount Earl receive from his grandmother when he turns 16
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Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
The slope of the line represented by the graph is -3
How to determine the slope of the lineFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following readings (when the lines representing the rise and the run are drawn)
Length of rise = -9
Length of run = 3
The slope of the line is then calculated as
Slope = Length of rise/Length of run
Substitute the known values in the above equation, so, we have the following representation
Slope = -9/3
Evaluate the quotient
Slope = -3
Hence, the line has a slope of -3
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the loth term of the arithmetic sequence 3x + 1, x + 4, -x + 7,
The 10th term of the arithmetic sequence will be x + 4
What is arithmetic sequence?An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.
If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:
The 10th term of the arithmetic sequence will be
= a + 9d
We are given the arithmetic sequence 3x + 1, x + 4, -x + 7,
where a = 3x + 4
d = x + 4- (3x + 1)
= x + 4 - 3x - 1
= -2x + 3
Therefore, a + 9d = 3x + 1 + (-2x + 3)
= 3x + 1 - 2x + 3
= 3x - 2x + 4
= x + 4
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Which of the following inequalities matches the graph?
x>4
x<4
y>4
v<4
The answer choice which correctly represent the inequality that matches the given graph as required is; y < 4.
Which inequality among the answer choices matches the graph?As evident in the task content; the given graph includes a shaded region whose boundary line is parallel to the horizontal axis and has a y-intercept; 4.
On this note, since the given border line is a broken line, it follows that the inequality sign is; > or <.
Ultimately, since the region below the line is shaded, the required inequality is; y < 4.
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In the table below, the x-values
are proportional to the y-values. Find
the missing y-value.
X
5
7
y
10
The value of y from the given table is 14.
What is a proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".
Given that, the x-values are proportional to the y-values.
Where, x=5 and y=10
Now, x=7
Here, x∝y
x=ky
5=10k
k=1/2
So, x=1/2y
y=2x
Substitute x=7 in y=2x, we get
y=14
Therefore, the value of y is 14.
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Here is a set of data.
2.4 1.6 3.2 0.3 1.5
a) Calculate the mean.
b) Each piece of data is increased by 10. Calculate the new mean.
c) Each new piece of data is now doubled. Calculate the new mean.
Answer:
a 1.8
b 11.8
c 23.6
Step-by-step explanation:
divide the sum of all values withing each data set by the number of values
y varies directly as x. If y = 6 when x = 3, find y when x = -33.
[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"y" varies directly with "x"}}{y=kx}\hspace{5em}\textit{we also know that} \begin{cases} y=6\\ x=3 \end{cases} \\\\\\ 6=k(3)\implies \cfrac{6}{3}=k\implies 2=k\hspace{5em}\boxed{y=2x} \\\\\\ \textit{when x = -33, what's "y"?}\qquad y=2(-33)\implies y=-66[/tex]
A number line shows
[tex]1 \frac{1}{4} [/tex]
,
[tex] - 2\frac{2}{4} [/tex]
and
[tex]1 \frac{3}{4} [/tex]
which statement is NOT true?
The statement which is not true; B [tex]1 \frac{1}{4} ,[/tex] is less than negative of [tex]- 2\frac{2}{4}[/tex] because [tex]1 \frac{1}{4} ,[/tex] is located to the right of - [tex]- 2\frac{2}{4}[/tex] on the number line.
What is a number line?Integers are arranged at equal intervals along horizontal straight lines called number lines. A number line can be used to represent every number in a series. The endpoints of this line go on forever. Some will have a defined beginning and end. It refers to those as closed number lines. Number lines might be alternatively left empty or blank. A number ladder is a vertical number line.
We need to find number line that shows [tex]1 \frac{1}{4} , - 2\frac{2}{4}[/tex] and - [tex]1 \frac{3}{4}[/tex]
which statement is NOT true;
A. [tex]1 \frac{1}{4} ,[/tex] is greater than negative of [tex]1 \frac{3}{4}[/tex] because [tex]1 \frac{1}{4} ,[/tex] is located to the right of - [tex]1 \frac{3}{4}[/tex] on the number line is true statement.
B. This is not true. [tex]1 \frac{1}{4} ,[/tex] is less than negative of [tex]- 2\frac{2}{4}[/tex] because [tex]1 \frac{1}{4} ,[/tex] is located to the right of - [tex]- 2\frac{2}{4}[/tex] on the number line.
The statement which is not true is Option B
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Which statements are true about the ordered pair (-4, 0) and the system of equations?
2c + y = -8
2-Y=-4
Select each correct answer.
1#
The ordered pair (-4, 0) is a solution to the first equation because it makes the first equation true.
#2
The ordered pair (-4, 0) is a solution to the second equation because it makes the second equation true.
3#
The ordered pair (-4, 0) is not a solution to
the system because it makes at least one of the equations false
4#
The ordered pair (-4, 0) is a solution to the system because it makes both equations true.
The given ordered pair satisfy the first as well as second equation thus option (A),(B) and (D) are correct.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
In another word, the equation must be constrained with some constraints.
As per the given system of equations,
2x + y = − 8
x − y = −4
Put (-4,0) in the above equations,
2(-4) + 0 = -8
-8 = -8 (Satisfied)
-4 - 0 = -4
-4 = -4 (Satisfied)
Since both are true thus both will be true.
Hence "Both the first and second equations are satisfied by the ordered pair that is presented.".
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The correct system of equations are followed as,
2x + y = − 8
x − y = −4
Dominic says that the product of 827 and 53 is 43,511. Is his answer
correct? Explain.
No, Dominic's answer is incorrect.
To find the product of 827 and 53, you can use the standard multiplication algorithm that you would use for decimal numbers.
First, you need to multiply the rightmost digit of 53, which is 3, by 827. This gives you 2481.
Then, you need to multiply the next digit of 53, which is 5, by 827 and add this result to the previous one. This gives you 43,811.
Therefore, the product of 827 and 53 is 43,811, not 43,511 as Dominic has stated. Dominic's answer is incorrect because he has made an error in the calculation.
"want to buy a car in 10 years' time. It will cost £10,000. How much money do I need to put in the bank today if the interest rate is 5% (per annum, compound)?"
A regular hexagonal prism having one side of base is 4cm and its height is 20cm,find its total surface area.
Use this formula
total surface area=lateral surface area+2base area
Or in short form
TSA=LSA+2BA
Answer as soon as possible
Answer:240√3cm³
Step-by-step explanation: The base is a regular hexagon. We can divide the base into 6 equilateral triangles.
Each equilateral triangle has side a=4cm. Hence the area of the base is B⇒ 6×√3÷4×4² ⇒ 24√3
This implies that V = B×h = 24√3 × 10 = 240√3cm³
Math 5th grade
The rule for an input/output table is output = x + 2
The output for the expression x+2 will be;
0 = 2
1 = 3
2 = 4
3 = 5
What are functions?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. Mapping or transformation is used to denote a function in math. These functions are usually denoted by letters such as f, g, and h. The domain is defined as the set of all the values that the function can input while it can be defined. The range is all the values that come out as the output of the function involved. Co-domain is the set of values that have the potential of coming out as outputs of a function.
Using the function Output = x + 2
For input x = 0
Output = 0 + 2
Output = 2
For input x = 1
Output = 1 + 2
Output = 3
For input x = 2
Output = 2 + 2
Output = 4
For input x = 3
Output = 3 + 2
Output = 5
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P=500 R=10% T=??? I=$10
Answer:
Given,
P=500
R=10percent
I=10
T=?
We know,
Time=100×i / R×P
= 100×10 / 10×500
= 1000/ 5000
= 5
therefore time is 5 years!!
What are the roots of the quadratic function f(q) = q^2- 125?
The roots of the given quadratic function are obtained as 5√5 and -5√5 respectively.
What is a quadratic equation?The general form of a quadratic equation is given as ax^2 + bx + c = 0.
Here, a ≠ 0 and b and c are integers.
The degree of a quadratic equation is 2.
The given quadratic function is f(q) = q² - 125
Its roots can be found by equating it to zero as,
q² - 125 = 0
Apply the identity a² - b² to factorize as,
⇒ (q - √125)(q +√125) = 0
⇒ (q - 5√5)(q + 5√5) = 0
⇒ q = 5√5, -5√5
Hence, the roots are given as 5√5 and -5√5 respectively.
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Solve the simultaneous equations
4x + 4y = 49
7x + 2y = 52
I just need to check my answers but can someone briefly explain how they got their answer
The values of x and y are 5.07 , 6.75 respectively .
What is linear Equation ?
linear equation can be defined as the equation in which the highest degree is one .
Given System of equations ,
4x + 4y = 49 let this be equation 1
7x + 2y = 52 let this be equation 2
multiply equation 1 with 7
and equation 2 with 4
so , we get ,
28x + 28y = 343
28x + 8y = 208
So, By subtracting both equations , we get
28y - 8 y = 343 - 208
20 y = 135
y = 135/20
y = 27/4
y = 6.75
Substitute y = 6.75 in the equation 2
we get,
7x + 2 * 6.75 = 52
7x = 50 - 14.50
7x = 35.50
x = 35.50 / 7
x = 5.07
Hence, The value of x and y are 5.07 , 6.75 respectively .
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Find the slope of the line graphed below.
Answer
-3/7
Step-by-step explanation:
What is the domain of the function y=√x+6-7
The domain of the function is x≥ -6. The correct option is B.
What are domain and range?The domain of a function is the set of values that can be plugged into it. This set contains the x values in a function like f. (x). A function's range is the set of values that the function can take. This is the set of values that the function returns after we enter an x value.
Given that the function is y=√(x+6) -7. Here the domain will be all the x values we can put in the function.
When the graph is plotted for the function we get the starting point of the function as (-6,-7). So the domain will be all the values from -6 to infinity.
The graph of the function is attached with the answer below.
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URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100
POINTS!!!
Answer:The measures of an exterior angle are 21,60°, and an interior angle is 360° in the given regular polygon with 14 sides.
Step-by-step explanation:
Denise created a decorative bowl for a display. She carved a piece of
wood into a cylinder with a diameter 15 inches and a height a of 5 inches.
a Then she carved a cone with a diameter of 12 inches and a height of 4
inches from the center of one base of the cylinder.
What is the approximate volume of the wood that forms the decorative
bowl?
The volume of the decorative bowl is V{B} = 233.25π.
What is the volume of a cylinder and a cone?The volume of a cylinder is equivalent to -
V{Cylinder} = πr²h
The volume of a cone is equivalent to -
V{Cone} = 1/3 πr²h
Given is that Denise created a decorative bowl for a display. She carved a piece of wood into a cylinder with a diameter 15 inches and a height a of 5 inches. Then she carved a cone with a diameter of 12 inches and a height of 4 inches from the center of one base of the cylinder.
We can write the volume of the decorative bowl as -
V{B} = V{Cylinder} - V{Cone}
V{B} = πr₁²h₁ - 1/3 πr₂²h₂
V{B} = π{r₁²h₁ - 1/3 r₂²h₂}
V{B} = π{7.5 x 7.5 x 5 - 1/3 x 6 x 6 x 4}
V{B} = π{281.25 - 48}
V{B} = 233.25π
Therefore, the volume of the decorative bowl is V{B} = 233.25π.
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What is the solution to this Equation?
Answer: C, 85
Step-by-step explanation:
Hopefully, that is a fourth root :)
Raise the entire equation to the fourth power.
x-4 = 3^4
x - 4 = 81
x = 85
Option C matches the answer
The following table gives you the distribution of marks secured by some students in anexamination. 0-20 21-30 31-40 41-50 51-60 61-70 71-80 no of students: 42 38 120 84 48 36 32 Find (i) Median marks (ii) the percentage of failures, if the minimum for a pass is 35 marks. (Ans. 40.5 and 30.5)
A recipe uses 3 cups of milk to make 6 servings. If the same amount of milk is used
for each serving, how many servings can be made from one gallon?
1 gallon = 4 quarts
1 quart
2 pints
1 pint
1 cup
-
T
= 2 cups
= 8 fluid ounces
Before you try that problem, answer the question below.
How many cups will you need to find the number of
servings for?
try
There are 32 servings that can be made from one gallon.
The given data as follows:
1 gallon = 4 quarts
1 quart = 2 pints
1 pint = 2 cups
1 cup = 8 fluid ounces
if 1 quart is 2 pints, then 4 quarts will be
= 4 × 2 = 8 pints
if 1 pint is 2 cups, then 8 pints will be
= 8 × 2 = 16 cups
Here 1 gallon is 16 cups
A recipe uses 3 cups of milk to make 6 servings.
The rate of servings to cups is 6 servings to 3 cups which is a unit rate of 2 servings per cup.
If 1 cup is 2 servings, then 16 cups will be
= 16 × 2 = 32 servings
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Help would be greatly appreciated!
Thank you!
Answer:
x>4
Step-by-step explanation:
the bar graph below represents the number of each type of animal found in northern Pennsylvania forest by a researcher. If the researcher moved to a larger central Pennsylvania forest with about 1,000 total animals , how many beats should the researcher expect to see?
The number of bears that the researcher should be expected to see in the larger central Pennsylvania forest with about 1,000 total animals is given as follows:
95 bears.
How to obtain the number of bears?To obtain the number of bears in the larger forest, first we must obtain the proportion in the smaller forest.
The proportion is given by the number of bears divided by the total number of animals, both of these amounts given by the bar graph presented at the end of the answer.
The number of bears is given as follows:
20.
The total number of animals is given as follows:
20 + 70 + 30 + 90 = 210.
Meaning that the proportion of bears is of:
20/210.
Hence, out of 1000 animals, the expected number of bears is of>
20/210 x 1000 = 20000/210 = 95 bears.
Missing InformationThe bar graph is given by the image presented at the end of the answer.
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