Using the unitary method, we found that Mary used 11 1/2 cups of flour altogether in the two recipes.
Mary had 6 3/4 cups of flour, which can be written as 27/4 cups of flour. We can multiply the whole number 6 by the denominator 4, which gives us 24. Adding the numerator 3 to this product gives us a total of 27. Therefore, 6 3/4 cups of flour is equivalent to 27/4 cups of flour.
Now that we have all the quantities in the same units, we can add them together. To add fractions, we need a common denominator. In this case, the common denominator is 4.
27/4 cups of flour + 5/2 cups of flour + 9/4 cups of flour
To add fractions, we need the denominators to be the same. We can rewrite 5/2 as an equivalent fraction with a denominator of 4 by multiplying the numerator and denominator by 2:
27/4 cups of flour + (5 * 2)/(2 * 2) cups of flour + 9/4 cups of flour
27/4 cups of flour + 10/4 cups of flour + 9/4 cups of flour
Now that we have a common denominator, we can add the numerators together:
(27 + 10 + 9)/4 cups of flour
46/4 cups of flour
To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 2:
46 ÷ 2 / 4 ÷ 2 cups of flour
23/2 cups of flour
Since 23/2 can be simplified further, we can express it as a mixed number:
23 ÷ 2 = 11 with a remainder of 1
So, the total amount of flour Mary used altogether is 11 1/2 cups.
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Complete Question:
Mary had 6 3/4 cups of floor. She used 2 1/2 cups of flour in one recipe and 2 1/4 cups of flour in another.
How much flour did she use altogether?
A political campaign wants to estimate the number of adult residents who voted in the last city election. Answer the following. (a) Which of the following surveys probably would best represent the entire adult population of the city? 25 homeowners are randomly selected; 14 voted in the last election. 25 adult residents are randomly selected from the city; 10 voted in the last election. 25 senior residents are randomly selected; 11 voted in the last election. (b) There are 20,600 adults who live in the city. Using your answer from part (a), estimate the number of adults who voted in the last city election.
Using sampling concepts, it is found that:
a) The best method is: 25 adult residents are randomly selected from the city;
b) The estimate is that 11,536 adults voted in the election.
What is sampling?It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.
In this problem, the sample will be representative if all adults, no matter if senior or not, homeowners or not are represented, hence the best method is:
25 adult residents are randomly selected from the city;
The estimate of the number of adults that voted is:
14/25 x 20,600 = 11,536.
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(Lesson 1.3) Use properties to find the sum or product. (3,5,7,9,11 only)
The values when the given numbers are multiplied will be:
230
78
3
91
1800
How to compute the values?3. 5 × 23 × 2
It should be noted that the given information simply means that we should multiply 5 by 23 by 2. This will be:
= 5 × 23 × 2
= 230
5. 34 + 0 + 18 + 26
This information simply means that we should add thirty four, eighteen, and twenty six together. This will be:
34 + 0 + 18 + 26 = 78
7. (3 × 10 × 8) = ....... × (10 × 8)
(3 × 10 × 8) = 3 × (10 × 8)
9. 0 + ...... = 91
It simply means the number that will be added to zero that will give ninety one. This will be 91.
11. The total income for the theater will be:
= (20 × 18) × 5
= 1800
Therefore, the correct values based on the computation will be 730, 78, 3, 91, and 1800.
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If you register a 0. 08 bac or refuse to take a breath test, your license will be automatically suspended for.
If you register a 0. 08 bac or refuse to take a breath test, your license will be automatically suspended for 12 months.
What is bac test?The amount of alcohol in your blood is determined via a blood alcohol(bac)test. The breathalyzer test, which police officers frequently administer to people they suspect of driving while intoxicated, is more widely known. While breathalyzers provide quick findings, they are not as precise as bac tests that measure alcohol in the blood.
The same 0.08 bac limit applies to adults in all 50 states who are 21 years of age or older, who are driving while intoxicated and breaching the law.
No amount of alcohol is safe when you are driving, even if your bac is below the legal limit. Don't drive after drinking, please!
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Write an equation of the line in slope-intercept form that is parallel to the line y= -4 + 2 and passes through (2,4)
Answer:
Step-by-step explanation:
If the lines are parallel, it means that the slopes are the same. To write an equation in the slope intercept form, we need the slope and the y-intercept. We are given the slope. We need to find the y-intercept. We can use the slope and the point to help us. The point is written in the form (x,y). In this case the point is (2,4) so we will use 2 for x and 4 for y.
y = mx + b Plug in what we know
4 = -4(2) + b b is what we are looking for. It is the y-intercept
4 = -8 + b Now add 8 to both sides
12 = b
Now we can write the equation:
y = -4x +12
ind the hypotenuse of the following triangle. [2]
This is a RIGHT ANGLE triangle!
c2 =a2 +b2
that's the rule
for example
c2=5^2+5^2
c2=25+25
c2=50 square root is
c=7.07^2
Using rigid motion, which statement is true about the triangles?
O ABC is congruent to FED
O ABC is congruent to FDE.
Ο Δ ABC is congruent to DEF.
triangles are not congruent
Answer:
ABC is congruent to DEF
Step-by-step explanation:
I think its this one cause the angles are the same
Let u - 4x? - 1. Find du. (4-1) du - Indicate how the limits of integration should be adjusted in order to perform the integration with respect to u. (Enter your answer using interval notation.) [0, 1] - Evaluate the definite integral. 01 Need Help? Read to a Tutor Consider the following. Let u = x + 1. Find du. du- Indicate how the limits of integration should be adjusted in order to perform the integration with respect to L. (Enter your answer using interval notation, [0, 2] - Evaluate the definite integral.
The value of du becomes 4 by integration.
According to the statement
we have given a two statement which are u - 4x and u = x + 1.
And we have to find the value of du by the use of integration.
An Integral assigns numbers to functions in a way that describes the data.
So,
From u - 4x
here du becomes by derivative
du - 4dx/du
du = 4dx/du. -(1)
And in u = x + 1.
here du becomes
du = dx/du -(2)
by comparing both terms from equation (1) and (2) we get the value of du
du = 4.
the value of du is 4.
So, The value of du becomes 4 by integration.
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Fill out First row is standard form
Second row is Factored Form already done for you.
Answer:
(x + 6)(x - 2) = x² + 4x - 12
(x + 2)(x - 8) = x² - 6x - 16
(x + 6)(x - 6) = x² - 36
(x - 5)(x - 1) = x² - 6x + 5
(x - 4)(x - 10) = x² - 14x + 40
(x + 2)(x + 5) = x² + 7x + 10
Step-by-step explanation:
Use FOIL.
(x + 6)(x - 2) =
F - first: x × x = x²
O - outer: -2 × x = -2x
I - inner: 6 × x = 6x
L - last: 6 × -2 = -12
(x + 6)(x - 2) = x² - 2x + 6x - 12
Now, combine like terms.
(x + 6)(x - 2) = x² + 4x - 12
(x + 2)(x - 8) = x² - 6x - 16
(x + 6)(x - 6) = x² - 36
(x - 5)(x - 1) = x² - 6x + 5
(x - 4)(x - 10) = x² - 14x + 40
(x + 2)(x + 5) = x² + 7x + 10
If the coordinates of two points are A (-3,5) and B (-9, -6), then find the value of (abscissa of A) + (ordinate of B)
Answer:
abscissa of A = -3
ordinate of B = -6
A+B = -3+(-6)= -3-6=
-9
What is equilibrium if autonomous expenditures are $2,000 and the mpe is 0. 5?
The equilibrium level if autonomous expenditures are $2,000 and the mpe is 0. 5 is $4000.
How to calculate the equilibrium?From the information given, the autonomous expenditures are $2,000 and the mpe is 0. 5.
Here, the equilibrium level will be:
= 2000/(1 - 0.5)
= 2000/0.5
= 4000
In conclusion, the correct option is $4000.
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I need help finding m
Answer:
i need this too hahahaha
Peter sells ice cream for a living. On Monday, his revenue was 150 dollars. On Tuesday, his revenue was 100 dollars. Finally, on Wednesday, his revenue was 50 dollars. How much is Peter's revenue so far?
Answer:
300 dollars
Step-by-step explanation:
Note that:
{Peter's revenue on Monday: 150 dollars
Peter's revenue on Tuesday: 100 dollars
Peter's revenue on Wednesday: 50 dollars}
---------------------------------------------------------------
In this problem, we need to find how much is Peter's revenue so far (total).
We need to use addition to determine how much Peter's revenue is in total.
So, add 150, 100, and 50.
We get 150 + 100 + 50 = 300
Finally, Peter's revenue in total is 300 dollars.
Answer:
$300
Step-by-step explanation:
add 150+100+50
=300
Triangle ABC Is shown on the coordinate plane.
What is the area of AABC?
OA 22.63 square units
OB. 24 square units
OC 48 square units
OD.
m. All rights reserved
16.97 square units
4
A(4.4)
-6
8-3,-3
6
42
A
42
4
-6-
C(3,3)
Answer: B
Step-by-step explanation:
Using the distance formula, we get the height is [tex]4\sqrt{2}[/tex].
Similarly, we get the base is [tex]6\sqrt{2}[/tex].
So, the area is [tex]\frac{1}{2}(4\sqrt{2})(6\sqrt{2})=24[/tex]
Here is a list of numbers: 2 , 8 , 1 , 7 , 4 , 10 , 1 , 15 , 20 State the median.
Answer:
7
Step-by-step explanation:
1, 1, 2, 4, 7, 8, 10, 15, 20
median = 7
Given that tanx=14 and sinx is negative, determine sin(2x), cos(2x), and tan(2x). Write the exact answer. Do not round.
By applying trigonometric identities, the value of tan(x) = 14, gives;
[tex]sin(2 \cdot x) = \frac{28}{197} [/tex]
[tex]cos(2 \cdot x) = -\frac{195}{197} [/tex]
[tex]tan(2 \cdot x) = -\frac{28}{195} [/tex]
Which method can be used to find the value of the trigonometric expressions?Given;
tan(x) = 14
sin(x) is negative
By definition, we have;
[tex]sin(2 \cdot x) = \mathbf{\frac{2 \cdot \: tan(x)}{1 + {tan(x)}^{2} }} [/tex]
Which gives;
[tex]sin(2 \cdot x) = \frac{2 \times 14}{1 + {14}^{2} } = \frac{28}{197} [/tex]
Similarly, we have;
[tex]cos(2 \cdot x) = \mathbf{\frac{1- tan(x)^2}{1 + {tan(x)}^{2} }} [/tex]
Which gives;
[tex]cos(2 \cdot x) = \frac{1- 14^2}{1 + {14}^{2} } = -\frac{195}{197} [/tex]
[tex]tan(2 \cdot x) = \mathbf{\frac{sin(2 \cdot x) }{cos(2 \cdot x) } } [/tex]
Which gives;
[tex]tan(2 \cdot x) = \frac{ \frac{28}{197}}{-\frac{195}{197} } = -\frac{28}{195} [/tex]
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The relationship between the natural variation and specifications is quantified by a measure known as the _____.
The relationship between the natural variation and specifications is quantified by a measure known as the Process capability index.
According to the questions,
The relationship between the natural variation and specifications is quantified by a measure known as the Process capability index.
Process capability index refers to the capability of a process to deliver output which lies within the specifications limits that are desired.
Hence, the relationship between the natural variation and specifications is quantified by a measure known as the Process capability index.
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Find the height of the basketball hoop to the nearest foot. a. 7 ft b. 10 ft c. 12 ft d. 15 f
The height of the basketball hoop to the nearest foot will be 12ft .
There are two ways to continue. The first method is to use trigonometric ratios.
You can use the tangent ratio because you have specified one leg and are trying to solve it with the other leg.
x equals the length of the other leg. .. Plug in known values.
Another way to find out is to monitor the angle. If the two angles are 45 degrees and 90 degrees, you can see that the third angle is 45 degrees. This makes it an isosceles triangle. That is, the other leg is 7 feet long.
2) Determine the height of the tire
Add 7 feet and 5 feet (human height):
7 + 5 = 12 feet
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help!>> Which is the best first step in solving the
absolute value inequality
-3 5x+6+1 >6?
Answer:
see explanation
Step-by-step explanation:
- 3 | 5x + 6 | + 1 ≥ 6
First step : subtract 1 from both sides
- 3 | 5x + 6 | ≥ 5
Which line plot correctly shows the data?
The line plot shown C in the figure is correct.
Given that the recorded lengths of ribbon pieces which is used in project is [tex]11\frac{1}{4},11\frac{1}{4},10\frac{3}{4},10\frac{1}{2},10\frac{7}{8},10\frac{5}{8},9\frac{7}{8},11\frac{1}{4}[/tex].
Frequency refers to the number of times an event or value occurs. A frequency table is a table that lists items and shows how many times those items occurred.
A line plot displays the data using a no. line.
Firstly, we will fimd the frequency of each value
Values Frequency
9 (7/8) 1
10(4/8)=10(1/2) 1
10(5/8) 1
10(6/8)=10(3/4) 1
10(7/8) 1
11(2/8)=11(1/4) 3
Option A is incorrect because 11(2/8) has no data values in the line plot (i.e. frequency = 0)
Option B is incorrect because 11(2/8) has no data values in the line plot (i.e. frequency = 0)
Option C is correct because the frequency distribution of the data is represented correctly in the line plot.
Option D is incorrect because 11(2/8) has 2 data values in the line plot (i.e., frequency = 2)
Hence, the line plot which correct shows the data is third line plot.
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The sunshade on one set of equipment has a square base of 120 cm and a height of 50 cm. The
sunshades are open-bottomed square based pyramids. This means that the base is not included.
a. Determine the total surface area, in m², of the sunshade.
The total surface area, in m², of the sunshade is 0.4344 m²
How to calculate surface area of a squared pyramid ?A pyramid can have a squared base, rectangular base or other polygons. The formula we can to find the total surface area of a squared pyramid is
Surface Area = P x l/2
Where
P = base parameterl = slant heightGiven that a sunshade on one set of equipment has a square base of 120 cm and a height of 50 cm. That means that the length L of the base will be 120 cm and half of it will be 60 cm
To find the slant height l, we will use Pythagoras theorem.
[tex]l^{2}[/tex] = 60² + 50²
[tex]l^{2}[/tex] = 3600 + 2500
[tex]l^{2}[/tex] = 6100
l = √6100
l = 78.1 cm
convert it to meter
l = 78.1/100
l = 0.781 m
The perimeter P of the base = 4 x 120/100 = 4.80 m
The Surface Area = P x l/2
Substitute all the necessary parameters into the formula
Surface Area = 4.80 x 0.781/2
Surface Area = 1.8744 m²
If the sunshades are open-bottomed square based pyramids, this means that the base is not included. That is, the area of the base should be taken away from the answer above.
Area of the base = 120/100 x 120/100 = 1.44 m²
The total surface area, in m², of the sunshade will 1.8744 - 1.44
The total surface = 0.4344 m²
Therefore, the total surface area, in m², of the sunshade is 0.4344 m²
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Can someone please help me with this similar area question? I have the answer but I’m not sure how to get to it. Will make brainliest!
Step-by-step explanation:
well there is a very simple point that you have mistaken tho:
484cm², 25cm²
Areas are defined in square cm but the radius is in cm
so:
[tex] \sqrt{ \frac{484 {cm}^{2} }{25 {cm}^{2} } } = \frac{7.92}{r} = = = > 4.4 = \frac{7.92cm}{x} = = > x = \frac{7.92cm}{4.4} = x = 1.8cm[/tex]
and there you go
What is the slope of a line passing through (-4,-5)
and (-2,-9)?
Answer:
slope = - 2
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 4, - 5 ) and (x₂, y₂ ) = (- 2, - 9 )
m = [tex]\frac{-9-(-5)}{-2-(-4)}[/tex] = [tex]\frac{-9+5}{-2+4}[/tex] = [tex]\frac{-4}{2}[/tex] = - 2
if the length of a rectangle is decreased by 2cm and the width is increased by 6 cm the result will be a square the area of this square will be 64 cm^2 greater than the area of a rectangle find the area
The area of the rectangle is 105 square cm
How to determine the rectangle area?Represent the dimensions of the rectangle with x and y
So, the length of the square would be:
Length = x - 2
Width = y + 6
The areas are then calculated as:
Rectangle = xy
Square = (x -2)(y + 6)
The relationship between the areas is:
(x -2)(y + 6) = 64 + xy
Expand
xy + 6x - 2y - 12 = 64 + xy
This gives
6x - 2y - 12 = 64
Add 12 to both sides
6x - 2y= 76
Divide through by 2
3x - y = 38
By trial by error, we have:
x = 15 and y = 7
The rectangle area is then calculated as:
Rectangle = xy
This gives
Rectangle = 15 * 7
Evaluate
Rectangle = 105
Hence, the area of the rectangle is 105 square cm
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What is the measure of Zz?
140°
80°
Z
Answer:
60
Step-by-step explanation:
140 = 80 + z
z = 60
Answer:
60°
Step-by-step explanation:
The whole angle is 140° and one side is 80°. Now, you just have to subtract 140 and 80 to get 60. I hope this helps!
Select all of the following problem situations that involve permutations. How many ways can you arrange 4 of the letters of the word SOLVE if no letter can be used more than once
There are 24 ways in which we can arrange 4 letters of the word "SOLVE" if no letter can be used more than once.
Given a word of 4 letters of the word "SOLVE".
We are required to find the number of ways the four letters of the word SOLVE if no letter can be used more than once.
Permutation is an arrangement of objects in a definite order of things.
Factorial of a number is the product of it and its lesser numbers upto 1.
Number of letters=4
Number of ways=4!
=4*3*2*1
=24 ways
Hence there are 24 ways in which we can arrange 4 letters of the word "SOLVE" if no letter can be used more than once.
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Explaining How to Compare Ratios Using Fractions Compare these three ratios using fractions. 3 to 2 5:6 8 to 12 Think about the steps you could take to compare the ratios using fractions. The first step is to write the ratios as fractions. The next step is to use a to rewrite the fractions. Finally, compare the to help you order the ratios.
A ratio is a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.
The parts of a fraction.In Mathematics, a fraction comprises two (2) main parts and these include:
NumeratorDenominator3 to 2 = 3/2
5:6 = 5/6
8 to 12 = 3/2
Thus, a common denominator of 12 can be used to rewrite the fractions and then you should compare the numerators to order the ratios in an ascending order.
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Step 1: Place the graph paper in landscape orientation. Measure from the top left hand corner 6 inches right and 5 inches down. This will be your starting point for
your diagram.
Step 2: Using a ruler and index card/protractor create an isosceles Right triangle. Drawing the triangles legs 1 inch straight up from the starting point and 1 inch to the
right of the starting point. Connect the endpoints of the two segments to create your right isosceles triangle.
Step 3: On a separate piece of paper, use the Pythagorean Theorem to calculate the length of the hypotenuse. You only need to do this for the first 8 if you discover a
pattern.
Step 4: Using your original Right triangle, add another leg measuring 1 inch and right angle to the hypotenuse of your original Right triangle. Connect the endpoints
to form a new hypotenuse for your new Right triangle.
Step 5: Show the calculations to find the length of the new hypotenuse.
Step 6: Continue to repeat this process of connecting and drawing new triangles with a side length of 1 inch, using the previous hypotenuse as the other side. Draw
triangles until you are able to measure the square root of 17. You must show all calculations (Step 3) on a separate piece of paper.
The right triangle whose hypotenuse is the square root of 17 has legs of 1 inch and 4 inches
How to determine the hypotenuse?Step 1 and 2: Create an isosceles right triangle
This is represented by the attached figure in (see figure 1 for this triangle)
The legs of this triangle have a length of 1 inch
Step 3: The hypotenuse
This is calculated using the following Pythagoras theorem
[tex]h^2 = 1^2 + 1^2[/tex]
This gives
[tex]h = \sqrt 2[/tex]
Step 4: Create another isosceles right triangle
This is represented by the attached figure in (see figure 2 for this triangle)
The legs of this triangle are 1 inch and 2 inches, respectively
This hypotenuse is calculated by:
[tex]h^2 = 2^2 + 1^2[/tex]
This gives
[tex]h = \sqrt 5[/tex]
Step 5: Create another isosceles right triangle
This is represented by the attached figure in (see figure 3 for this triangle)
The legs of this triangle are 1 inch and 3 inches, respectively
This hypotenuse is calculated by:
[tex]h^2 = 3^2 + 1^2[/tex]
This gives
[tex]h = \sqrt {10[/tex]
Step 6: Create another isosceles right triangle
This is represented by the attached figure in (see figure 4 for this triangle)
The legs of this triangle are 1 inch and 4 inches, respectively
This hypotenuse is calculated by:
[tex]h^2 = 4^2 + 1^2[/tex]
This gives
[tex]h = \sqrt{[17[/tex]
See that the hypotenuse is the square root of 17
Hence, the right triangle whose hypotenuse is the square root of 17 has legs of 1 inch and 4 inches
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What is the area of the triangle?
Enter your answer in the box.
in²
Right triangle with sides forming the right traingle labeled 25 inches and 60 inches and the side across from the right angle labeled 65 inches.
Using it's formula, the area of the right triangle is of 750 inches squared.
What is the area of a right triangle?The area of a right triangle is given by half the multiplication of the two legs, which are the two smaller sides.
In this problem, the two legs are 25 inches and 60 inches, hence the area of the triangle is:
A = 0.5 x 25 x 60 = 750 inches².
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Hello Brainly Teacher Brainly Moderators and trusted helpers!
Answer:
P(x < 84) = 0.3085 or approximately 31%============
Hello to you from Brainly team!
GivenMean grade μ = 86,Standard deviation σ = 4,Grade limit x = 84.To find Probability of that a randomly selected grade is less than 84 or P(x < 84).SolutionFind z-score using relevant equation:
z = (x - μ)/σSubstitute values and calculate:
z = (84 - 86)/4 = - 0.5Using the z-score table find the corresponding P- value.
P(x < 84) = 0.30854 or approximately 31%Answer:0.30854
Step-by-step explanation:Solution:
Given:
Using the z-scores formula;
From the z-scores table, the probability is;
Therefore, the probability that the grade is less than 84 is 0.30854
which facts are true for the graph of the function below check all that apply F(x)=log6x
Based on the graph of the function (F(x) = log6x), the following facts are true:
It is increasing. The x-intercept is (1, 0). What is a graph?A graph is a type of chart that is used to graphically represent data on both the horizontal and vertical lines of a Cartesian coordinate i.e x-axis and y-axis.
By critically observing the graph of the function (F(x) = log6x) attached in the image below, we can infer and logically deduce that its domain and range include all real numbers that are greater than 0 (x > 0).
This ultimately implies that, the following facts are true:
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Complete Question:
Which facts are true for the graph of the function below? Check all that apply. F(x) = log6 x
A. It is increasing.
B. The range is y > 0.
C. The x-intercept is (1, 0).
D. It is decreasing.
E. The y-intercept is (0, 6).
F. The domain is x > 6.