Answer: Let's call the first term of the arithmetic sequence "a", and the common difference between the terms "d".
Then, we know that the sum of the first 8 terms is 88, so we can write:
a + (a + d) + (a + 2d) + ... + (a + 7d) = 88
Using the formula for the sum of an arithmetic sequence, we can simplify this to:
8a + 28d = 88
We also know that the product of the 1st and 8th terms is 120, so we can write:
a(a + 7d) = 120
Now we have two equations with two variables. We can solve for one of the variables in terms of the other and substitute into the other equation to solve for the remaining variable.
Solving the first equation for d:
d = (88 - 8a)/28
Substituting into the second equation:
a(a + 7[(88-8a)/28]) = 120
Multiplying both sides by 28 to eliminate the fraction:
28a^2 + 154a - 960 = 0
We can factor this quadratic equation as:
(2a - 15)(14a + 64) = 0
So either 2a - 15 = 0 or 14a + 64 = 0. Solving for "a" in each case, we get:
a = 15/2 or a = -64/14
Since we're looking for the first term of the sequence, which must be positive, we can discard the negative value and conclude that the first term is:
a = 15/2
Therefore, the first term of the arithmetic sequence is 7.5.
Step-by-step explanation:
QUICK, ANSWER THIS QUESTION FOR 30 POINTS!!!!
Which of the following is the equation in slope-intercept form for the line that passes through the points (-4, 1) and (-3, 0)?
Answer:
y= -x - 3 is correct
Step-by-step explanation:
PLS 100PTS
WILL MARK AS BRAINLIEST
a ladder 20m long, leaning against a vertical wall makes an angle of 40⁰ with the horizontal ground. with the aid of a sketch diagram, determine the distance of the foot of the ladder from the wall (write your answer to 2 decimal places)
To determine the distance of the foot of the ladder from the wall, we can use trigonometry. Let's call the distance we want to find "x".
First, let's draw a diagram:
|\
| \
20 | \ x
| \
|____\
40°
In this diagram, the ladder is the hypotenuse of a right triangle, and the distance we want to find ("x") is one of the legs. The other leg is the height of the ladder on the wall, which we don't need to know in order to solve the problem.
We can use the trigonometric function for the sine of an angle to relate the angle of elevation to the distance "x" and the length of the ladder:
sin(40°) = x / 20
To solve for "x", we can multiply both sides by 20:
20 sin(40°) = x
Using a calculator, we can evaluate the sine of 40 degrees to get:
20 sin(40°) ≈ 12.85
So the distance of the foot of the ladder from the wall is approximately 12.85 meters, rounded to two decimal places.
For what values of x does the graph of f(x) have a horizontal tangent? (Enter your answers as a comma-separated list.)
f(x) = x³ + 7x² + x + 1
X=
The point in which f(x) have a horizontal tangent are (-7 + √46)/3, (-7 - √46)/3
What values of x does f(x) have a horizontal tangentTo find the values of x where the graph of f(x) has a horizontal tangent, we need to find where the derivative of f(x) is equal to zero (since the derivative gives the slope of the tangent line).
First, we find the derivative of f(x):
f'(x) = 3x² + 14x + 1
Next, we set f'(x) equal to zero and solve for x:
3x² + 14x + 1 = 0
Using the quadratic formula, we get:
x = (-14 ± √(14² - 431)) / (2*3)
x = (-14 ± √(184)) / 6
x = (-14 ± 2√46) / 6
Simplifying:
x = (-7 ± √46) / 3
Therefore, the values of x where the graph of f(x) has a horizontal tangent are (-7 + √46)/3 and (-7 - √46)/3.
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A well that pumps at a constant rate of 78,000 ft³/d has achieved equilibrium so that there is no change in the drawdown with time. The well taps an unconfined aquifer that consists of sand overlying impermeable bedrock at an elevation of 260 ft ASL. An observation well 125 ft away has a head of 277 ft ASL; another observation well 385 ft away has a head of 291 ft ASL. Compute the value of hydraulic conductivity using the Thiem equation.
Therefore, the value of hydraulic conductivity using the Thiem equation is approximately 10.67 ft/day.
What is equation?An equation is a mathematical statement that indicates that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The expressions on both sides of the equation are separated by an equal sign "=" which means that the two expressions have the same value. Equations are used to model relationships between variables, solve problems, and make predictions in various fields of science, engineering, economics, and mathematics. They are an essential tool in algebra, calculus, and other branches of mathematics.
Here,
To compute the value of hydraulic conductivity using the Thiem equation, we need to substitute the given values into the equation:
K = (Q / π) * ((h2 - h1) / log(r2/r1))
where:
Q = pumping rate = 78,000 ft³/d
h1 = head at the pumping well = 260 ft ASL
h2 = head at the observation well 385 ft away = 291 ft ASL
r1 = distance from the pumping well to the observation well 125 ft away = 125 ft
r2 = distance from the pumping well to the observation well 385 ft away = 385 ft
Substituting the values, we get:
K = (78,000 / π) * ((291 - 260) / log(385/125))
K = 10.67 ft/day
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Let U={2,3,4,5,6,7,8,9,10,11), A = {3,5,7,9,11}and B = {7,8,9,10,11}. Use this information to answer the following questions
A-B
(A-B)^c
U-(A-B)^c
(AUB)^c
(A^cUB^c)^c
Using set theory, the element in each of the set are, A - B = {3, 5}, (A - B)^c = {2, 4, 6, 7, 8, 9, 10, 11}, U - (A - B)^c = {3, 5}, (A \cup B)^c = {2, 4, 6} and (A^c U B^c)^c = {7, 9, 11}.
What is the element in each set?The given sets are:
U = {2,3,4,5,6,7,8,9,10,11}
A = {3,5,7,9,11}
B = {7,8,9,10,11}
We can use these sets to find the following:
1. A - B: The elements in set A that are not in set B are {3, 5}.
2. (A - B)^c: The complement of set A - B in U contains all the elements in U that are not in A - B. These elements are {2, 4, 6, 7, 8, 9, 10, 11}.
3. U - (A - B)^c: This set contains all the elements in U that are not in the complement of A - B. These elements are {3, 5}.
4. (A U B)^c: This set contains all the elements in U that are not in the union of sets A and B. The union of A and B is {3, 5, 7, 8, 9, 10, 11}, so the complement is {2, 4, 6}.
5. (A^c U B^c)^c: This set contains all the elements in U that are in neither the complement of set A nor the complement of set B. The complement of set A is {2, 4, 6, 8, 10} and the complement of set B is {2, 3, 4, 5, 6}. The union of these two sets is {2, 3, 4, 5, 6, 8, 10}, so the complement of this set in U is {7, 9, 11}.
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What is Jane's hourly rate? * (1 Point) HAMBURGER PALACE ENTERPRISES, INC. PAYROLL ENDING 3/14/09 NAME JANE BROWN EMPLOYEE NO. L4325 EARNINGS Description Hrs. Amount Tax Regular CURRENT YTD 20 120.00 120.00 1650.00 CHECK NO. 9343 Medicare AMOUNT $87.50 TAXES WITHHELD Fed Income Tax Social Sec State Income Tax Current YTD Description 12.72 174.90 MEALS 7.44 102.30 1.74 3.60 23.93 OTHER DEDUCTIONS 49.50 Amount 7.00
So, Jane's hourly rate is $6.00 per hour.
What is division?In mathematics, division is a basic arithmetic operation that involves splitting a number or quantity into equal parts or groups. It is the inverse operation of multiplication, where we find out how many times one number (the divisor) can fit into another number (the dividend) without leaving any remainder.
Here,
However, we can calculate her hourly rate by dividing her total earnings by the number of hours she worked.
From the payroll information provided, Jane earned $120.00 for 20 hours of work. Therefore, her hourly rate would be:
Hourly rate = Total earnings / Number of hours worked
Hourly rate = $120.00 / 20 hours
Hourly rate = $6.00 per hour
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A $40,000 car depreciates in value at a rate of 36% per year. The
value, V, after t years can be modeled by the function V =
40,000(0.64). Which function is equivalent to the original function?
. V = 40,000(0.8)St
V=40,000(0.8)2t
V = 40,000(0.8)
V = 40,000(0.8)
The correct function equivalent to the original function V = 40,000(0.64) is V = 40,000(0.64)ⁿ.
What is percent?Percent is a way of expressing a fraction or a decimal as a fraction of 100. It is denoted by the symbol "%". For example, the fraction 3/4 can be written as 75% and the decimal 0.5 can be written as 50%. Percentages are commonly used in everyday life to express values such as discounts, interest rates, and success rates.
Here,
The original function V = 40,000(0.64) models the value, V, of a $40,000 car after t years, where the car depreciates at a rate of 36% per year. The expression 0.64 represents the remaining value of the car after one year, which is obtained by subtracting 36% from 100% (i.e., 100% - 36% = 64%).
To find an equivalent function, we need to simplify 0.64. We can write 0.64 as 0.8², since 0.8 multiplied by itself gives 0.64.
So, V = 40,000(0.64) is equivalent to V = 40,000(0.8²), which simplifies to V = 40,000(0.64). This means that both expressions represent the same function that models the value of the car after t years, given that the car depreciates at a rate of 36% per year.
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Use the given information to find the unknown value.
2. y varies
1. y varies directly as the square root
inversely with the cube of x.
of x. When x = 16, then y = 4. Find y
y = 1. Find y when x = 1.
when x = 36.
When x = 3, then
3. The distances that an object falls varies directly with the
square of the time, t, of the fall. If an object falls 16 feet in one
second, how long for it to fall 144 feet?
4. The rate of vibration of a string under constant tension varies
inversely with the length of the string. If a string is 24 inches long
and vibrates 128 times per second, what is the length of a string
that vibrates 64 times per second?
Applying the definition of variation, we have:
1. When x = 36, y = 6.
2. When x = 1, y = 27.
3. It takes 3 seconds for the object to fall 144 feet.
4. Length of a string that vibrates 64 times per second is 48 inches.
What is an Inverse Variation?Inverse variation is a type of relationship between two variables in which one variable increases while the other decreases, or vice versa, in a way that the product of the two variables remains constant.
In other words, if we have two variables x and y that are inversely proportional, we can write:
x × y = k, where k is a constant.
1. We are given that y varies directly as the square root of x. This means that we can write:
y = k√x
where k is a constant of proportionality. To find the value of k, we can use the given information that when x = 16, y = 4:
4 = k√16
4 = 4k
k = 1
Now we can use this value of k to find y when x = 36:
y = 1√36
y = 6
Therefore, when x = 36, y = 6.
2. We are given that y varies inversely with the cube of x. This means that we can write:
y = k/x³
where k is a constant of proportionality. To find the value of k, we can use the given information that when x = 3, y = 1:
1 = k/3³
1 = k/27
k = 27
Now we can use this value of k to find y when x = 1:
y = 27/1³
y = 27
Therefore, when x = 1, y = 27.
3. We are given that the distance that an object falls varies directly with the square of the time, t, of the fall. This means that we can write:
d = kt²
where d is the distance, k is a constant of proportionality, and t is the time. To find the value of k, we can use the given information that when t = 1, d = 16:
16 = k(1)²
16 = k
k = 16
Now we can use this value of k to find the time it takes for the object to fall 144 feet:
144 = 16t²
9 = t²
t = 3
Therefore, it takes 3 seconds for the object to fall 144 feet.
4. We are given that the rate of vibration of a string under constant tension varies inversely with the length of the string. This means that we can write:
r = k/L
where r is the rate of vibration, L is the length of the string, and k is a constant of proportionality.
To find the value of k, we can use the given information that when L = 24 inches, r = 128 vibrations per second:
128 = k/24
k = 3072
Now we can use this value of k to find the length of a string that vibrates 64 times per second:
64 = 3072/L
L = 48 inches
Therefore, the length of a string that vibrates 64 times per second is 48 inches.
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If 3000 dollars is invested in a bank account at an interest rate of 4 per cent per year,
Find the amount in the bank after 6 years if interest is compounded annually:
Find the amount in the bank after 6 years if interest is compounded quarterly:
Find the amount in the bank after 6 years if interest is compounded monthly:
Finally, find the amount in the bank after 6 years if interest is compounded continuously:
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{\underline{annually}, thus once} \end{array}\dotfill &1\\ t=years\dotfill &6 \end{cases} \\\\\\ A = 3000\left(1+\frac{0.04}{1}\right)^{1\cdot 6} \implies A \approx 3795.96 \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{\underline{quarterly}, thus four} \end{array}\dotfill &4\\ t=years\dotfill &6 \end{cases} \\\\\\ A = 3000\left(1+\frac{0.04}{4}\right)^{4\cdot 6} \implies A \approx 3809.20 \\\\[-0.35em] ~\dotfill[/tex][tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{\underline{monthly}, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &6 \end{cases} \\\\\\ A = 3000\left(1+\frac{0.04}{12}\right)^{12\cdot 6} \implies A \approx 3812.23 \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$3000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &6 \end{cases} \\\\\\ A = 3000e^{0.04\cdot 6} \implies A \approx 3813.75[/tex]
help me please this hard
Answer: -1/2
Step-by-step explanation:
To find the slope: rise/run
starting from the point (0,2), you go up 1 to reach the line
Therefore 1 is your rise.
Then go right 2 units and you hit the line again.
Therefore the slope is 1/2.
But the linear line is going downwards, so it is a negative slope
Therefore your final answer is:
-1/2
You and your four friends buy tickets to a baseball game. The total cost is $70. Write and solve an equation to find the total cost of each ticket.
Answer: 14 dollars.
Step-by-step explanation:
You (1) + your four friends (4) is 5.
5 times a number is 70.
5x=70
70/5=14
x=14
I will mark you brainiest!
What is the area of a rectangle with a length of 3 cm and a width of 4.5 cm?
A) 1.5 cm2
B) 6.75 cm2
C) 7 cm2
D) 13.5 cm2
Answer:
A equals 13.5 centimeters
What is the total interest on a 4-year term loan of
$1,700 with a simple annual interest rate of 8%?
A. $544
B. $554
C. $564
D. $574
Answer:
a
Step-by-step explanation:
The formula to calculate simple interest is:
I = P * r * t
Where:
I = Interest
P = Principal amount
r = Rate of interest
t = Time period
Given:
Principal amount (P) = $1,700
Rate of interest (r) = 8% per annum
Time period (t) = 4 years
Using the formula of simple interest:
I = P * r * t
I = 1,700 * 0.08 * 4
I = $544
Therefore, the total interest on a 4-year term loan of $1,700 with a simple annual interest rate of 8% is $544.
Answer: A. $544
Write an equation for a rational function with the given characteristics.
Vertical Asymptotes at x= -2 and x=4, x-intercepts at (-4,0) and (2,0), horizontal asymptote at y= -3.
Enclose numerators and denominators in parentheses. For example (a-b)/(1+n).
Include a multiplication sign between symbols. For example, a*x.
F(x) =
An equation for a rational function with the given characteristics is found as: f(X) = a(x+4)(x) / (x+2)(x-4).
Explain about the rational function?Any function that can be expressed as a polynomial divided by such a polynomial is said to be rational. The domain of either a rational function is just the set of all numbers besides the zeros of the denominator since polynomials are specified everywhere.As x = -2 and X = 4 have vertical asymptotes, the denominator will contain the equations (x+2) and (x-4)
The terms (x+4) and 1 will be in the numerator since the x intercepts are (-4,0) , respectively (x-0).
Our current formula is f(X) = a(x+4)(x) / (x+2)(x-4)
We examine the horizontal asymptote to determine the value of A.
The limit of a function as x -> infinity would be - 3 since the horizontal asymptote reflects what the function looks like as x approaches infinity.
Thus, an equation for a rational function with the given characteristics is found as: f(X) = a(x+4)(x) / (x+2)(x-4)
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Identify the value for the variable.
What is the value of x in this simplified expression?
7-9-7-3-7x
x=
What is the value of y in this simplified expression?
114
= 11
118
y=
Answer: x=7 y=5
Step-by-step explanation:
I believe this is the answer to the question
pelase help quick 25 points it 6th grade math
The median shows that the average number of students per middle school classroom in both districts is 24, while the mean shows that the average number of students per middle school classroom in one district is 24 and the other is 25.
What is median?Median is the middle value of a set of data. It is the value that divides the data set into two equal halves. It is an important measure of central tendency and is used to compare sets of data.
The difference between the mean number of students per middle school classroom in each school district is 2 students. The difference between the median number of students per middle school classroom in each school district is 0 students.
Based on the number of students shown for each school district, the median would provide the most accurate picture of the number of students in a middle school classroom, as there are some extreme values that would affect the mean but not the median.
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i-ready an 80-ounce bottle of apple juice contains 32 ounces of water what percent of the bottle of apple juice is wayer
The percent of the bottle of apple juice is 40%.
What is a percentage, and how is it different from a fraction or a decimal?An element of a whole number is a fraction. There are many different kinds of fractions. Three-quarters, for instance, is a fraction.
A decimal point separates a fractional component from an integral component to form a decimal. In the decimal 2.5, for instance, the fractional portion comes after the decimal point and is followed by the integer 2, which is put before it.
Per cent simply means one in a hundred. Hence, it is a number with a fractional representation that has a denominator of 100. As a result, fractions of a whole number are also described using percentages.
Given that, 80-ounce bottle of apple juice contains 32 ounces of water.
Thus,
% of water = (32 / 80) * 100 = 40%
Hence, the percent of the bottle of apple juice is 40%.
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Maurice can weed the garden in 45 minutes. Olinda can weed the garden in 50 minutes, how long would it take them to weed the garden if they work together
Tt would take Maurice and Olinda approximately 47.37 minutes
What is work done?
Work done in physics is the dot product of force and displacement. When a force applied on an object results in a displacement, it is said to be work is done on the object.
Let's denote the time it takes both Maurice and Olinda working together to weed the garden as t.
We can use the formula: 1 / t = 1 / a + 1 / b
Plugging in the given values, we get: 1 / t = 1 / 45 + 1 / 50
1 / t = (50 + 45) / (50 * 45) = 95 / 2250
Then, we can invert both sides of the equation to get: t / 1 = 2250 / 95
Simplifying the right-hand side by dividing both the numerator and the denominator by 5, we get:
t = 2250 / 95 = 47.37 minutes (rounded to two decimal places)
Therefore, it would take Maurice and Olinda approximately 47.37 minutes to weed the garden if they work together.
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Suppose you send about 12 text messages a day and your older sister sends more text messages than you do . together you send a total of about 26 messages per day. about how many text messages does she send a day ? Write an equation and solve for the unknown value
Let x be the number of text messages that your older sister sends per day. Then we can write an equation based on the given information:
x + 12 = 26
We can solve for x by subtracting 12 from both sides of the equation:
x = 26 - 12
x = 14
Therefore, your older sister sends about 14 text messages per day.
Help me! I need help with my homework !
Answer:
Rounding to the nearest hundredth, the area of the shaded region is approximately 167.91 square yards.
Step-by-step explanation:
To find the area of the shaded region between two circles with the same center, we need to subtract the area of the smaller circle from the area of the larger circle.
The area of the larger circle is:
A_outer = πr_outer^2
= π(11.9 yd)^2
≈ 445.03 yd^2
The area of the smaller circle is:
A_inner = πr_inner^2
= π(9.4 yd)^2
≈ 277.12 yd^2
Therefore, the area of the shaded region is:
A_shaded = A_outer - A_inner
≈ 445.03 yd^2 - 277.12 yd^2
≈ 167.91 yd^2
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consider the function.
f(x)= √x
g(x)= √x-3+1
h(x)= √x+1-2
which statement compares the relative locations of the minimums of the functions?
The correct statement regarding the relative minimums of each function is given as follows:
The minimum of h(x) is farther left and down from the minimums of f(x) and g(x).
What are the relative minimums of each function?The function f(x) is defined as follows:
f(x)= √x.
It has a relative minimum at (0,0), which is one the first quadrant.
The function g(x) is defined as follows:
√x-3+1
It is a translation of 3 units right and 1 unit up of f(x), hence the minimum has coordinates (3,1), which is on the first quadrant.
The function h(x) is defined as follows:
h(x)= √x+1-2
It is a translation of 1 unit left and 2 units down of f(x), hence the minimum has coordinates (-1, -2), which is on the third quadrant.
The third quadrant is farther left and down from the first quadrant.
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LOTS OF POINTS HELP ASAP!
The time between the injections that is injected again when the dosage reaches 9 is solved to be 1.8 to the nearest tenth
How to find the time between the injectionsThe information given by the problem include the expression
D(h) = 20e^(-0.45h)
The expression is an exponential function that shows the relationship between time and the dosage in milligrams
given that D = 9 we find h
D(h) = 20e^(-0.45h)
9 = 20e^(-0.45h)
9/20 = e^(-0.45h)
take ㏑ of both sides
㏑(9/20) = -0.45h
isolating h by dividing by -0.45
h = ㏑(9/20) / -0.45
h = 1.774
h = 1.8 to the nearest tenth
This shows that the time is 1.8 hours
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HELP
Recipe:
Cinnamom Rolls
makes 12 rolls
1/4 -ounce package active dry yeasy
1 cupt warm water
3 tablespoons molasses
1/3 cup powedered milk
1 egg yolk,beaten
1 egg white, beaten
3 1/2 cups bread flour, divided
6 tablespoons butter, melted and divided
1 teaspoon salt
1/2 cup whole wheat flour
1/3 cup raisins
1 large egg, beaten
1/4 cup water
You will use the recipe above to answer the following questions:
Respond to the questions about the second recipe:
This recipe makes 12 rolls, but you need to make 30 rolls. What number will you need to multiply the amount of each ingredient by to adjust the recipe? How did you determine this number?
How many ounces of yeast will you need to make 30 rolls?
How many cups of powdered milk will you need to make 30 rolls?
How many tablespoons of butter will you need to make 30 rolls?
How many more cups of bread flour than whole wheat flour will you need to make 30 rolls?
Notice that the original recipe calls for
1
4
cup of water. If you put in
3
8
cup of water, by how much have you
To adjust the recipe to make 30 rolls instead of 12, we need to multiply the amount of each ingredient by a factor of 30/12 = 2.5.
What is factor?A factor is a number or expression that divides another number or expression evenly without a remainder.
According to question:To adjust the recipe to make 30 rolls instead of 12, we need to multiply the amount of each ingredient by a factor of 30/12 = 2.5.
To determine this factor, we divide the desired number of rolls (30) by the original number of rolls (12):
2.5 = 30/12
To find the amounts of each ingredient needed to make 30 rolls, we multiply the original amounts by 2.5:
Yeast: 1/4 oz x 2.5 = 0.625 oz (or about 0.63 oz)
Warm water: 1 cup x 2.5 = 2.5 cups
Molasses: 3 tbsp x 2.5 = 7.5 tbsp (or about 1/2 cup + 1 tbsp)
Powdered milk: 1/3 cup x 2.5 = 0.83 cups (or about 3/4 cup + 1 tbsp)
Egg yolk: 1 beaten yolk x 2.5 = 2.5 beaten yolks (or about 2 yolks)
Egg white: 1 beaten white x 2.5 = 2.5 beaten whites (or about 2 whites)
Bread flour: 3 1/2 cups x 2.5 = 8.75 cups (or about 8 3/4 cups)
Butter: 6 tbsp x 2.5 = 15 tbsp (or about 1 cup - 1 tbsp)
Salt: 1 tsp x 2.5 = 2.5 tsp (or about 2 1/2 tsp)
Whole wheat flour: 1/2 cup x 2.5 = 1.25 cups (or about 1 1/4 cups)
Raisins: 1/3 cup x 2.5 = 0.83 cups (or about 3/4 cup + 1 tbsp)
To make 30 rolls, you will need 0.625 oz (or about 0.63 oz) of yeast.
To make 30 rolls, you will need 0.83 cups (or about 3/4 cup + 1 tbsp) of powdered milk.
To make 30 rolls, you will need 15 tbsp (or about 1 cup - 1 tbsp) of butter.
To make 30 rolls, you will need 8.75 cups (or about 8 3/4 cups) of bread flour, which is 8.75 - 1.25 = 7.5 cups more than the 1.25 cups of whole wheat flour needed.
If you put in 3/8 cup of water instead of the 1/4 cup called for in the original recipe, you have added an extra 3/8 - 1/4 = 1/8 cup of water, or 2 tablespoons of water.
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Quick Math Answer ok
Which of the following is the number 316.72 written in scientific notation?
A.
B. 3.1672 × 10²
C.
3.1672 x 10-2
D.
3.1672 x 103
3.1672 10
E. 3.1672 × 10-³
We can rewrite 3.1672 × 10¹² as 3.1672 × 10² The correct option is A
How to write a number in scientific notation ?First we first express it as a number between 1 and 10 multiplied by a power of 10. In this case, 316.72 can be expressed as:
3.1672 × 10¹² (since we move the decimal point 2 places to the right to get to 31672)
However, in scientific notation, the exponent should represent the number of places the decimal point is moved. Since we moved the decimal point to the right, the exponent should be negative.
Therefore, we can rewrite 3.1672 × 10¹² as:
3.1672 × 10²
So, the answer is (A).
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A rectangle has an area of 60 square inches and the length is 4 inches more than the width. Find the length and width of the rectangle
Answer:
w = 6in, l = 10in
Step-by-step explanation:
Area of a rectangle is [tex]A=l*w[/tex]
and [tex]l = 4 + w[/tex]
We can solve for length and width by substituting these values for the equation.
[tex]60in^2=(4+w)*w[/tex]
[tex]60in^2=4w+w^2[/tex]
[tex]0 = w^2 + 4w + 60in^2[/tex]
factor out the equation.
[tex]0= (w+10)(w-6)[/tex]
therefore w = 6in (tossing out the negative solution)
which means
[tex]l = 4 + w[/tex]
[tex]l = 6in + 4[/tex]
l = [tex]10in[/tex]
Hope this helps!
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PLS HELP DUE TOMORROW!!
Answer:
Step-by-step explanation:
[tex]V=\pi r^2 h[/tex]
Substitute [tex]h=l,r=2,V=150,[/tex] we get
[tex]150=\pi \times 2^2 \times l[/tex]
[tex]150=4\pi l[/tex]
[tex]l=\frac{150}{4\pi}=11.94cm[/tex]
The following chart shows the number of rows in an auditorium and the total number of seats. Find an equation that defines the number of seats with respect to the number of rows
Answer:
Step-by-step explanation:
[tex]S=40R+20[/tex]
help im doing the math diagnostic
Answer: -5 1/4
Step-by-step explanation:
After answering the final question incorrectly, Sandra's score will be -5 1/4 in fraction form, and -5.25 in decimal form. This is because every time Sandra gets a question wrong her grade goes down by -3/4 points. And -4 1/2 minus -3/4 is -5 1/4. I hope this helped. If not, let me know and I can try to reword it.
Answer: b
Step-by-step explanation: