The correct answer is "b. t-test for a single sample". This hypothesis-testing procedure is used to determine whether a sample mean is significantly different from a known population mean when the population variance is unknown.
The correct answer is "b. t-test for a single sample". This hypothesis-testing procedure is used to determine whether a sample mean is significantly different from a known population mean when the population variance is unknown. The t-test for a single sample is a statistical test that compares the sample mean to a hypothetical population mean, using the t-distribution. It helps researchers determine whether the sample mean is a reliable estimate of the population mean, or whether the difference between the two means is due to chance.
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Simplify:
[tex]\frac{a^3-2a^2-15a}{a^3+a^2-30a}[/tex]
Answer:
Step-by-step explanation:
[tex]\frac{a^{3}-2a^{2}-15a }{a^{3}+a^{2}-30a} =\frac{a^{2}-2a-15}{a^{2}+a-30}[/tex]
[tex]\frac{a^{2}-2a-15}{a^{2}+a-30}=\frac{(a-5)(a+3)}{(a-5)(a+6)}= \frac{(a+3)}{(a+6)}[/tex]
What are the 5 properties of inequality?
The set of properties for inequalities is as follows:
1. Additive characteristics of inequality
2. Inequality's subtraction property
3. The inequality's multiplication property
4. The unequal division property
5. Converse Property
An inequality is a relationship between two expressions that can be described mathematically and can be represented by any of the following symbols: >, <, ≤, ≥, =, and ≠.
The set of properties for inequalities is as follows:
1. Additive characteristics of inequality: The inequality remains the same even if both sides are given the same value.
2. Inequality's subtraction property: The inequality remains the same even after deducting the same amount from each side of it.
3. The inequality's multiplication property: Take p and q, two positive numbers. When p and q are both multiplied by the same positive value, the inequality stays the same. However, the inequality changes when p and q are both multiplied by the same negative value.
4. The unequal division property: Take p and q, two positive numbers. When p and q are both divided by the same positive number, the inequality is unaffected. However, the inequality is reversed when p and q are split by the same negative value.
5. Converse Property: According to the converse property, all we need to do to reverse the inequality symbol is flip the number.
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what is interesting in chapter exponents and powers
So on solving provided question we can say that the exponent will be as follows [tex]e^{x^{-2y}} = e^{x^{3}} = e^{34}[/tex].
what are exponents?Exponentiation, often known as "b raised to the nth power," is a mathematical operation denoted by the symbol bn that involves two numbers: a base number, b, and an exponent, or power, n. Exponents show how many times a number has been multiplied by itself. As an illustration, 2-3 (written as 23) denotes: 2 x 2 x 2 = 8. 23 is not equivalent to 2 + 3 = 6. Recall that an integer raised to the power of one equals itself. A approach to express huge numbers as powers is through the use of exponents. Exponent, then, is the quantity that indicates how many times a number has been multiplied by itself. As an illustration, 6 is multiplied by 4 to provide 6 x 6 x 6 x 6. It may be expressed as 64. 4 is where
the given exponent is
[tex]e^{x^{-2y}} = e^{x^{3}} = e^{34}[/tex]
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Manuel and Ruben both have bank accounts. The table represents the balance, y, for each account after x weeks. Which system of equations represents the table?
y = 11.5x and y = –13x
y = 11.5x + 218 and y = –13x + 22
y = 11.5x + 22 and y = –13x + 218
y = 22x + 11.5 and y = 218x – 13
The system of Equation the tables represent are:
y = 11.5x + 22 and y = –13x + 218
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Manuel:
slope = (33.50- 22)/ (1-0)
slope = 11.5
So, the Equation for Manuel
y- 22= 11.5 (x- 0)
y- 22 = 11.5x
y= 11.5x + 22
Ruben:
slope = (205- 218)/ (1-0)
slope = - 13
So, the Equation for Ruben
y- 218= -13 (x- 0)
y- 218 = -13x
y= -13x + 218
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3. Chris makes monthly donations to a public
radio station. Each month, the station
automatically deducts the same amount from
his checking account. The change in his
account balance with each deduction is
-$18.75. Which value represents the change in
Chris's account balance for his donations over
1.5 years?
A. -$181.25
B. -$237.50
C. -$281.25
D. -$337.50
Given the formula for simple interest: i=Prt, answer the following.
(Remember, i=interest, P=the principal amount, r=the interest rate per year as a decimal, t=time in years)
If the interest paid was $37.50 on a principal of $1500 for 6 months, what was the interest rate?
Give a numeric answer only with the percentage rate (NOT the decimal rate). Do not include work, units, or explanation. If necessary, round your answer to the nearest hundredth.
Answer:
I= PTR/100 where P=Principal, T = Time period in years, R = Rate of interest per annum.
The lines graphed below are parallel. The slope of the red line is - What is
3
the slope of the green line?
m=
O A. - 13/3
B. 3/1
OB.
O
c. - 3/1
D. 437
5
The slope of the green line is -4/3.
The correct option is C.
What is the slope of the line?
The slope of a line is a measure of how steep the line is and the direction it is going. It is defined as the ratio of the "rise" (the change in the y-coordinate) to the "run" (the change in the x-coordinate) between two points on the line.
The slope of a line is often represented by the letter "m" and can be calculated using the following formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line.
It is given that the lines graphed below are parallel.
We know that if two line having slopes m₁ and m₂ are parallel, then
m1 = m2
In other words, the slopes of two parallel lines are the same.
The slope of the red line is -4/3 and it is parallel to the green line. It means the slope of red and green line are the same.
The slope of green line = Slope of the red line
The slope of the green line = -4/3
Hence, The slope of the green line is -4/3.
The correct option is C.
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The slope of the green line is -4/3. The correct option is C.
What is the slope of the line?
The slope of a line is a measure of how steep the line is and the direction it is going. It is defined as the ratio of the "rise" (the change in the y-coordinate) to the "run" (the change in the x-coordinate) between two points on the line.
The slope of a line is often represented by the letter "m" and can be calculated using the following formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line.
It is given that the lines graphed below are parallel.
We know that if two line having slopes m₁ and m₂ are parallel, then
m1 = m2
In other words, the slopes of two parallel lines are the same.
The slope of the red line is -4/3 and it is parallel to the green line. It means the slope of red and green line are the same.
The slope of green line = Slope of the red line
The slope of the green line = -4/3
Hence, The slope of the green line is -4/3.
The correct option is C.
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The length of the base of an isosceles triangle is x. The length of a leg is x. The perimeter of the triangle is. Find x.
If the perimeter of the isosceles triangle is 12 cm, then the base of the triangle (x), as well as the length of the triangle leg (x) is 4 cm.
An isosceles triangle is a type of triangle in which two sides have the same length. These two equal sides are referred to as the legs of the triangle, while the remaining side is known as the base.
The perimeter of a triangle is the sum of the lengths of all its sides. In this case, since the triangle is isosceles, the base and one leg have the same length (x), and the other leg also has the same length (x). Therefore, the perimeter of the triangle is 2x + x = 3x. Given that the perimeter of the isosceles triangle is 12 cm, then:
3x = 12
x = 12/3
x = 4
So, the base and legs of the isosceles triangle each have a length of 4 cm.
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Your question seems to be missing the value for the perimeter of the triangle, but I suppose the complete question was:
"The length of the base of an isosceles triangle is x. The length of a leg is x. The perimeter of the triangle is 12 cm. Find x."
Jaycee created a figure by drawing a right
triangle next to a rectangle.
10 cm
-20 cm-
-15 cm-
What is the area of the figure in square
centimeters?
The area of the figure, which has a triangle and a rectangle with the same height, is 275 cm2.
what is rectangle ?You may also refer to it as a quadrilateral that is equiangular, meaning that all of its angles are equal. The parallelogram could alternatively have a straight angle. Rectangles with four sides that are all the same size are called squares. Four 90-degree vertices and equal parallel sides make up a quadrilateral with the rectangular shape. A rectangle is also referred to as a parallelogram since its opposing sides are parallel and equal.
given
Area of Figure = Area of Rectangle + Area of Triangle
= l*b+ 1/2*b*h
= 10 * 20 * 1/2 * 15 * 10
= 275cm2
The area of the figure, which has a triangle and a rectangle with the same height, is 275 cm2.
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The formula for the area of a rhombus is a = d1d2, where d1 and d2 are the lengths of the diagonals. Which are equivalent equations? select two correct answers. D1 = 2ad2 d1 = d2 = d2 = d2 = 2ad1.
The formula for the area of a rhombus is a = d1d2, where d1 and d2 are the lengths of the diagonals. The equivalent equation is d1 = 2A/d2 and d2 = 2A/d1.
The formula for rhombus area is as follows:
A= 1/2 d1d2
where d1d2 and are the rhombus's diagonals.
The comparable expressions must be found.
Because A = 1/2 d1d2
We must first eliminate the denominator 2, regardless of whether we need to construct the corresponding statement in terms of d1 or d2. When we multiply the two sides of the previous equation by two, we get
2A = d1d2
So, the equivalent expressions are d1 = 2A/d2 and d2 = 2A/d1
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Why does the acute angles in a right triangle determine the ratio of the side lengths?
Answer:
Step-by-step explanation:
If two right triangles share an acute angle measure, they are similar by angle-to-angle similarity. Corresponding side length ratios in the triangle are the same. The ratio of the side lengths of a right triangle depends only on the acute angle.
Adalyn is stocking up on cans of soup for the winter. They are on sale for $2.25 each and she has a $3 coupon. If she can spend no more than $30 on soup, how many cans can she buy?
Using simple mathematical operations, we know that Adalyn can purchase 14 cans if she spends no more than $30.
What are mathematical operations?An operation is a function in mathematics that transforms zero or even more input values into a clearly defined output value.
The firm's arity is influenced by the number of operands.
Most people believe that addition, subtraction, multiplication, and division are the four basic operations in mathematics.
So, we know that:
Money =30 + 3 = 33
Price per can 2.25.
Then, she can buy:
33/2.25 = 14.67
Round off to 14 cans.
Therefore, using simple mathematical operations, we know that Adalyn can purchase 14 cans if she spends no more than $30.
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Kara is building a sandbox shaped like a kite for her nephew. The top two sides of the sandbox are 29 inches long. The bottom two sides are 25 inches long. The diagonal DB has a length of 49 inches. What is the length of the diagonal AC
The length of diagonal AC is 54.8 inches when two sides are 29inches and 25 inches long.
How is this determined?To find the length of diagonal AC in the kite-shaped sandbox, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the length of the hypotenuse (the longest side) is equal to the square root of the sum of the squares of the other two sides.
How to use the Pythagorean Theorem?Identify the right triangle. In this case, we can see that the right triangle is formed by diagonal DB and the two sides of length 25 inches, which we'll call side a.
Substitute the known values into the formula, where AC is the hypotenuse and a and DB are the other two sides of the triangle: AC^2 = a^2 + DB^2
Solve for AC by taking the square root of both sides: AC = √(a^2 + DB^2)
Substitute the given values for a and DB: AC = √(25^2 + 49^2) = √(625 + 2401) = √3016 = 54.8
It's important to note that the kite shape can be considered as two congruent right triangles. The sides 25 and 29 are the legs, and the diagonal DB (49 inches) is the hypotenuse of one of the triangles. Since the triangles are congruent, their hypotenuse will have the same length. Therefore, the diagonal AC, which is the hypotenuse of the other triangle, also has a length of 49 inches.
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20.25 ➗ 0.9 standard form
The value of 20.25 ÷ 0.9 in standard form is 2.25×10¹
What is standard form?The standard form of a number is a way of writing the number in a form that follows certain rules. Any number that can be written as a decimal number, between 1.0 and 10.0, multiplied by a power of 10, is said to be in standard form.
This means that writing a value in the form 35.77× 10³ is very wrong in standard form because 35.77 is less than 10. But instead we write it in the form 3.577×10⁴, now 3.577 is less than 10.
The value of 20.25÷ 0.9 = 22.5
but this is not in standard form because 22.5 is greater than 10. By putting it in standard form, we divide it by 10 and multiply it by 10 again
This means that 22.5 = 2.25×10¹
Therefore 20.25 ÷ 0.9 in standard form is 2.25 × 10¹
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Mariu buy computer for £915. 00 each and ell them for £2081. 00 each. What i hi total profit on the ale of 13 computer?
Mariu buy computer for £915. 00 each and ell them for £2081. 00 each. then the total profit on the ale of 13 computer is £15158.00
What is a simple definition of profit?
the excess of returns over expenditure in a transaction or series of transactions. especially : the excess of the selling price of goods over their cost. 3. : net income usually for a given period of time.
The profit on the sale of 1 computer is the difference between the selling price and the buying price.
Profit on 1 computer:
£2081.00 - £915.00 = £1166.00
The profit on 13 computers is 13 times the profit on 1 computer.
13 × £1166.00 = £15158.00
£15158.00
hence Mariu buy computer for £915. 00 each and ell them for £2081. 00 each.then the total profit on the ale of 13 computer is £15158.00
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please help me i dont really know it
The length of line WX in both rectangles is 10.5 ft. The right option is (D) 10.5.
What is a rectangle?A rectangle is a plane shape with fours sides, having two opposite sides equal and parallel.
To calculate the length of WX, we use the formula below.
Note: Rectangle RSTV is similar to rectanngle WXYZ. And the ratio of their corresponding Lengths are equal.
Formula:
RV/WZ = RS/WX.................. Equation 1From the question,
Given:
RV = 2 ftWZ = 5 ftRS = 4.2 ftSubstitute these values into equation 1 and solve for WX
2/5 = 4.2/WXWX = (5×4.2)/2WX = 10.5 ftHence, the length of line WX is 10.5 ft
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What is the area of the trapezoid shown? Express your answer in simplest exact form. [asy] unitsize(1.5cm); pair a=(0,0); pair b=(1,sqrt(3)); pair c=(3,sqrt(3)); pair d=(4,0); draw(a--b--c--d--a); label("2",(a+b)/2,NW); label("2",(b+c)/2,N); label("2",(c+d)/2,NE); label("~$60^\circ$",a,NE); label("$60^\circ$~",d,NW); [/asy]
The area of the trapezium shown is 57.97 cm²
What is an equation?An equation is an expression that shows the relationship between variables and numbers.
The area for a two dimensional shape is the amount of space occupied for that shape.
The area of a trapezium is given by:
Area = (1/2)(sum opposite base) * height
For the trapezium shown, the parallel sides have a measure of 17 inches and 31 inches respectively. The height is 11.7 inches:
Area = (1/2)(7.9 + 10.8)(6.2) = 57.97 cm²
The area is 57.97 cm²
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What is the value of 3b - 5c if b = 5 and c =2
Therefore , the solution of the algebraic expression is the value of 3b - 5c when b = 5 and c = 2 is 5
What is the algebraic expression?An algebraic expression is a mathematical phrase that can contain numbers, variables, and mathematical operations. It represents a mathematical relationship, but it does not have a specific value. Algebraic expressions can be simple or complex, and they can be used to represent mathematical concepts or to perform calculations.
Here,
To find the value of 3b - 5c when b = 5 and c = 2, we can substitute these values into the expression and simplify it.
Given 3b - 5c = 3(5) - 5(2) = 15 - 10 = 5
Hence, the value of 3b - 5c when b = 5 and c = 2 is 5
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The Ratio Of A Screen's Width to it's height is 4:3.
The height of the screen is 24 cm.
What is it's width in centimetres (cm)?
Answer:
The height is 32
Step-by-step explanation:
The ratio of width to height is
4:3
We know the height is 24 so to go from 3 to 24 is multiplying by 8.
Multiply all terms by 8
4 * 8 : 3 * 8
32: 24
The ratio of the width to height is
32:24
The height is 32
=================================================
Work Shown
width/height = 4/3
w/24 = 4/3
3w = 24*4
3w = 96
w = 96/3
w = 32 cm is the width
-------------------
Another approach.
The ratio of width to height is 4:3, meaning a screen that has width 4 cm and height 3 cm is possible. Instead, we want the "height 3 cm" to be "height 24 cm". This is a jump of "times 8".
Multiply both parts of that ratio by 8 to get...
4:3
8*4:8*3
32:24
A screen that is 32 cm wide and 24 cm tall will give us a ratio 4:3 when simplifying fully.
The order of the numbers is important. We have the width listed first simply because it was listed first in the phrasing "ratio of width to height".
Roni and Allie are mowing the grass at the soccer field. Roni has a riding lawn mower and can mow the field in 30 minutes. Allie is pushing a lawn mover and can mow the field in 75 minutes. If Roni and Allie work together to mow the field, what part of the field would Roni mow?
The part of the field would Roni mow will be 4 3/7 of the field.
How to calculate the fraction?To find out what part of the field Roni would mow if he and Allie worked together to mow the field, you would need to calculate their combined rate of mowing.
You can find the combined rate by adding the rates of each person working alone:
Combined rate = (Roni's rate) + (Allie's rate)
Combined rate = (1/30 hour) + (1/75 hour) = (5/150) + (2/150) = (7/150) hour
Then divide the rate of Roni by the combined rate to find the proportion of the field that Roni would mow:
(Roni's rate) / (Combined rate) = (1/30 hour) / (7/150 hour) = (30/7) / 1 = 4.2857142857142856
So Roni would mow about 4.29 or roughly 4.3/7 of the field if he and Allie worked together.
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A triangle has angle measurements 24 and 85. What is the measure of the remaining angle?.
The measure of the remaining angle is 71 degrees.
The measure of the remaining angle in a triangle can be found by subtracting the sum of the measures of the other two angles from 180 degrees.
Key points:
The sum of the measures of the angles in a triangle is always 180 degrees.In any triangle, if one angle is known, the measure of the other two angles can be found by subtracting their measures from 180 degrees.In this specific case, the triangle has two angles with measures of 24 degrees and 85 degrees.The measure of the remaining angle can be found by subtracting the sum of the measures of the first two angles (24 + 85) from 180.The measure of the remaining angle is 71 degrees.Learn more about triangles here:
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please help me ill mark brainly
10points!
Answer:
x = 35°
Step-by-step explanation:
AC is a straight line with the 3 angles lying on it summing to 180°, so
∠ E + ∠ D + ∠ G = 180°
55° + ∠ D + 90° = 180°
145° + ∠ D = 180° ( subtract 145° from both sides )
∠ D = 35°
then
x and ∠ D are vertically opposite angles and are congruent, thus
x = 35°
What is the value of x in the equation 1.5 x 4 )- 3?
The value of x in the equation 1.5 (x + 4) - 3 = 4.5 (x - 2) is 4.
The BODMAS rule is a rule used to simplify a mathematical equation. BODMAS itself is an abbreviation of the Bracket, Order, Division, Multiplication, Addition, and Subtraction. This rule indicates the sequence in which a mathematical equation should be solved.
As we want to find the value of x, firstly we have to simplify the equation by applying the BODMAS rule to the given equation:
1.5 (x + 4) - 3 = 4.5 (x - 2)
Since there's no Bracket, Order dan Division part that can be solved, so the first step is applying the Multiply part:
1.5x + 6 - 3 = 4.5x - 9
Then we apply the addition and subtraction part:
1.5x - 4.5x = - 9 - 6 + 3
- 3x = - 12
x = 4
Thus, the value of x in the equation 1.5 (x + 4) - 3 = 4.5 (x - 2) is 4.
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A rectangle has a length of 5x+2 and a width of 3x - 1. If x=10, what is the perimeter and area?
Answer:
Perimeter = 162 units
Area = 1508 square units
Step-by-step explanation:
Given expressions:
Length = 5x + 2Width = 3x - 1If x = 10, then:
Length = 5(10) + 2 = 52Width = 3(10) - 1 = 29The formula for the perimeter of a rectangle is:
P = 2(w + l)where w is the width and l is the length.
Therefore, the perimeter of the rectangle is:
[tex]\implies \sf P = 2(29 + 52)[/tex]
[tex]\implies \sf P = 2(81)[/tex]
[tex]\implies \sf P = 162\;units[/tex]
The formula for the area of a rectangle is:
A = w · lwhere w is the width and l is the length.
Therefore, the area of the rectangle is:
[tex]\implies \sf A=29 \cdot 52[/tex]
[tex]\implies \sf A=1508\;square\;units[/tex]
Answer:
Area of rectangle = 1508
Perimeter of rectangle = 162
Step-by-step explanation:
Now we have to,
→ find the perimeter and area.
→ where x = 10.
Perimeter of rectangle is,
→ P = 2 × (L + W)
→ P = 2 × (5(10) + 2 + 3(10) - 1)
→ P = 2 × (50 + 2 + 30 - 1)
→ P = 2 × 81
→ [ P = 162 ]
Area of rectangle will be,
→ A = L × W
→ A = (5(10) + 2) × (3(10) - 1)
→ A = (50 + 2) × (30 - 1)
→ A = 52 × 29
→ [ A = 1508 ]
Hence, these are the values.
96.458 is between which two numbers?
Answer: 96 and 97
Step-by-step explanation:
Please answer
really urgent
Answer:
128 дней (days)
Step-by-step explanation:
5375/42 = 128 (округляем)
Answer:
128 days
Step-by-step explanation:
To solve this problem, we simply have to divide the total amount of oil in the tank by the amount of oil used each day.
[tex]5375 \textrm{ liters} \times \dfrac{1 \textrm{ day}}{42 \textrm{ liters}} = \dfrac{5375}{42} \textrm{ days} \approx 128 \textrm{ days}[/tex]
So, the tank will be empty after 128 days.
Note that the number of days is approximate; normally when measuring in the real world, whole numbers are used, as decimals in certain contexts (like in this situation) are confusing. So to simplify our answer, we can simply round up to 128 because by the end of the 128th day, the tank will be empty.
5x ( 2x^2 - 3x ) + 2x^3 - x^2
Answer:
[tex]12x^3-16x^2[/tex]
Step-by-step explanation:
[tex]10x^3-15x^2+2x^3-x^2=12x^3-16x^2[/tex]
PLS HELLP!!!! Cate has 2 cups of rice She divides it into 1/8cups how many servings of rice does she have?
Number of servings Cate can have is given by the equation A = 16 servings
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of servings be represented as A
Now , the equation will be
The number of cups of rice Cate has = 2 cups
The number of cups of servings Cate divides = 1/8 cups
So ,
The number of servings A = number of cups of rice Cate has / number of cups of servings Cate divides
Substituting the values in the equation , we get
The number of servings A = 2 / ( 1/8 )
On simplifying the equation , we get
The number of servings A = 2 x 8
The number of servings A = 16 servings
Therefore , the value of A is 16 servings
Hence , the number of servings is 16 servings
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Liz answered 47 of the 50 questions on a geography test correctly. What is her percent?
Answer: 94%
Step-by-step explanation:
solution: 47/50 as a percent is 94%
Is x3 an exponential function?