If four out of 12 people chose milk, then 8 did not choose milk, resulting in a fractional part of 2/3 representing those who chose other drinks.
Explanation:If four of 12 people chose milk, we can calculate the fractional part of the group that chose other drinks. We subtract the number of people who chose milk from the total number of people surveyed:
12 (total people) - 4 (people who chose milk) = 8 (people who chose other drinks).
The fractional part of the group that chose other drinks is therefore the number of people who chose other drinks divided by the total number of people:
8 (people who chose other drinks) / 12 (total people) = 2/3.
Two-thirds of the group chose drinks other than milk.
Learn more about Fractional Part here:https://brainly.com/question/32862511
#SPJ2
You are serving bratwurst and hamburgers at your annual picnic. You want at least three bratwursts or hamburgers for each of your 40 guests. Bratwursts cost $1.35 each and hamburgers $1.2 each. Your budget is $175.
Let x be the number of bratwursts and y the number of hamburgers. whiichs system of inequalities represents this situation?
Options:
x+y<=40 1.35x+1.2y>=175
x+y<=40 1.35x+1.2y<=175
x+y>=120 1.35x+1.2>=175
x+y>=120 1.35x+1.2<=175
...?
Answer:
Option D -[tex]x+y\geq 120[/tex] , [tex]1.35x + 1.2y \leq 175[/tex]
Step-by-step explanation:
Given : You want at least three bratwursts or hamburgers for each of your 40 guests. Bratwursts cost $1.35 each and hamburgers $1.2 each. Your budget is $175.
To find : Which system of inequalities represents this situation?
Solution :
Let x be the number of bratwursts and y the number of hamburgers.
You want at least three bratwursts or hamburgers for each of your 40 guests.
i.e, you want at least [tex]3\times(40)=120[/tex] bratwursts or hamburgers.
We can write the equation as,
Number of bratwursts + number of hamburgers at least 120
[tex]x+y\geq 120[/tex]
Bratwursts cost $1.35 each and hamburgers cost $1.2 each. Your budget is $175.
We can write equations as ,
Cost of bratwursts + cost of hamburgers at most 175
[tex]1.35x + 1.2y \leq 175[/tex]
Therefore, The system of linear equation form is [tex]x+y\geq 120[/tex], [tex]1.35x + 1.2y \leq 175[/tex]
Hence, Option D is correct.
PLZZZZZ HELP
Which answer best describes the system of equations shown in the graph?
not enough information
consistent and independent
coincident
inconsistent
Answer:
Option (2) is correct.
The given system of equation is Consistent and independent.
Step-by-step explanation:
coincident : When two lines overlap each other. then they are coincident lines.Inconsistent: When there is no solution for the given system of equations then the system is called "inconsistent". Consistent : When there is one or infinitely many solutions for the given system of equations is called "consistent".Independent : When each equation of the system gives new information Otherwise they are called Dependent. like x + y = 2 and 2x + 2y =4 this shows one equation is multiple of other hence, dependent.Now consider the given graph,
Since, they intersect at a unique point. Hence, they are consistent.
Also the two given equations are independent of each other .Thus, independent also.
Thus, the given system of equation is Consistent and independent.
Thus, option (2) is correct.
some one factor 5x^2+23x+26
5*x^2-23*x-(-26)=0
1. x = 2
2. x = 13/5 = 2.600A souvenir maker wants to create a scale model of the Empire State Building. The Empire State Building is 1,472 feet tall and has a base with dimensions 286 ft by 286 ft. If the model is 6 in. tall, what are the approximate dimensions of its base in inches? (Round your answer to the nearest tenth of an inch.)
A) 1.2 in. by 1.2 in.
B) 1 in. by 1 in.
C) 0.2 in. by 0.2 in.
D) 2.3 in. by 2.3 in.
If there is a ratio of 3 to 2 what is the ratio of 3if the total is 30
Find the product for 7 x 2/3
The word product is the answer to a multiplication problem.
7 x 2/3
7/1 x 2/3
(7 x 2)/(1 x 3)
Answer: 14/3
Find the radius of a circle with circumference of 55.3 yd^2. Round to the nearest tenth.
A retailer charges a flat handling fee of $5.00, plus $0.75 per quarter pound, to ship an item. Bailey pays $9.50 to have an item shipped from the retailer. What is the weight of the item? 1.50 pounds
Answer:
1.50 pounds
Step-by-step explanation:
Given : A retailer charges a flat handling fee of $5.00, plus $0.75 per quarter pound, to ship an item.
Bailey pays $9.50 to have an item shipped from the retailer.
To Find: What is the weight of the item?
Solution:
He paid total amount = $9.50
A flat handling fee = $5.00
Amount he paid without handling fee = $9.50-$5.00
=$4.50
Now we are supposed to find what is the weight of an item that costs $4.50
So, we are given that it costs $0.75 per quarter pound, to ship an item.
So, cost of 1 pound = [tex]\frac{0.75}{\frac{1}{4}}=3[/tex]
So, it cost $3 for 1 pound
So, weight of an item that costs $1 = [tex]\frac{1}{3}[/tex]
So, weight of an item that costs $4.50=[tex]\frac{1}{3}\times 4.50[/tex]
=1.50 pounds
Hence the weight of the item is 1.50 pounds.
Answer:
1.50 pounds
Step-by-step explanation:
el de arriba lo dijo
(URGENT-15 Points) Can someone help me/check my answers for this? Thank you! For the first screenshot, my answers for 1-5 are: (1) 79.2 (2) 12.4 (3) 78 and 82 (4) 76 and 84 (5) 74 and 86. I am stuck on questions 6-8 (#8 is on the second screenshot at the top...). On the second screenshot, I'm not sure how to answer question (9) based on the dot-plot on the first screenshot. For (10), if it's asking for the mean of these numbers, I got 23.8. If it's just asking for the sum, I got 119. For 11-12, the means aren't the same because this mean (#10) is based on the random sample generated from the original number of grades, while the first mean (#2) was based on the total population of grades for the entire class. It would make sense that the second mean would be smaller than the first. I'm giving away 15 points to the person who can help me with this and check my answers! I'd really appreciate it! :)
(-1,5),(0,6),(-1,7),(2,9) what is the domain range and is it a function ?
Solve -2.5n + 8.7 > 5.45.
n < 1.3
n > 1.3
n < -5.66
n > -5.66
Answer:
N < 1.3
Step-by-step explanation:
Go thank the answer above! :)
Carrots sell for $2.10 per pound, and crackers sell for $2.90 per pound. Glen bought some carrots and some crackers. The total weight was 2.3 pounds and cost $6.03.
How many pounds of carrots and how many pounds of crackers did Glen buy?
Note: Please give a direct answer
Sheila deposited $1,050.00 into a saving account at her local bank. if the interest rate is 1.5%, then how much will he have after 18 months (round your answer to the nearest cent)?
How many permutations of the letters ABCDEFG contain:
a.) the string BCD?
b.) the string CFGA?
c.) the strings BA and GF?
The number of permutations of ABCDEFG containing BCD, CFGA, and BA & GF are 120, 24, and 120, respectively.
Explanation:In permutations, the order of the items is important. For all these problems, we're asked how many permutations of the letters ABCDEFG contain a specific string. To solve this, we can initially treat the required string as a single item.
For BCD, we consider 'BCD' as one letter, so now we have 5 letters (A,E,F,G,BCD). The number of permutations for 5 items is 5P5 = 5! = 120. For CFGA, we consider 'CFGA' as one letter, so now we have 4 letters (B,D,E,CFGA). The number of permutations for 4 items is 4P4 = 4! = 24. For BA and GF, we consider 'BA' and 'GF' as one letter each, so now we have 5 letters (C,D,E,BA,GF). The number of permutations for 5 items is 5P5 = 5! = 120. Learn more about Permutations here:https://brainly.com/question/23283166
#SPJ12
Twice a number decreased by 44 is 6 times the sum of the number and 3 times the number. find the number
how do you solve:
5x^2 + 25x - 70
3.1 Pull out like factors :
5x2 - 25x - 70 = 5 • (x2 - 5x - 14)
3.2 Factoring x2 - 5x - 14
The first term is, x2 its coefficient is 1 .
The middle term is, -5x its coefficient is -5 .
The last term, "the constant", is -14
Step-1 : Multiply the coefficient of the first term by the constant 1 • -14 = -14
Step-2 : Find two factors of -14 whose sum equals the coefficient of the middle term, which is -5 .
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and 2
x2 - 7x + 2x - 14
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-7)
Add up the last 2 terms, pulling out common factors :
2 • (x-7)
Step-5 : Add up the four terms of step 4 :
(x+2) • (x-7)
Which is the desired factorization
4.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
4.2 Solve : 5 = 0
This equation has no solution.
A a non-zero constant never equals zero.
4.3 Solve : x+2 = 0
Subtract 2 from both sides of the equation :
x = -2
4.4 Solve : x-7 = 0
Add 7 to both sides of the equation :
x = 7
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula
Parabola, Finding the Vertex : 5.1 Find the Vertex of y = x2-5x-14
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 2.5000
Plugging into the parabola formula 2.5000 for x we can calculate the y -coordinate :
y = 1.0 * 2.50 * 2.50 - 5.0 * 2.50 - 14.0
or y = -20.250
Root plot for : y = x2-5x-14
Axis of Symmetry (dashed) {x}={ 2.50}
Vertex at {x,y} = { 2.50,-20.25}
x -Intercepts (Roots) :
Root 1 at {x,y} = {-2.00, 0.00}
Root 2 at {x,y} = { 7.00, 0.00}
5.2 Solving x2-5x-14 = 0 by Completing The Square .
Add 14 to both side of the equation :
x2-5x = 14
Now the clever bit: Take the coefficient of x , which is 5 , divide by two, giving 5/2 , and finally square it giving 25/4
Add 25/4 to both sides of the equation :
On the right hand side we have :
14 + 25/4 or, (14/1)+(25/4)
The common denominator of the two fractions is 4 Adding (56/4)+(25/4) gives 81/4
So adding to both sides we finally get :
x2-5x+(25/4) = 81/4
Adding 25/4 has completed the left hand side into a perfect square :
x2-5x+(25/4) =
(x-(5/2)) • (x-(5/2)) =
(x-(5/2))2
Things which are equal to the same thing are also equal to one another. Since
x2-5x+(25/4) = 81/4 and
x2-5x+(25/4) = (x-(5/2))2
then, according to the law of transitivity,
(x-(5/2))2 = 81/4
We'll refer to this Equation as Eq. #5.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x-(5/2))2 is
(x-(5/2))2/2 =
(x-(5/2))1 =
x-(5/2)
Now, applying the Square Root Principle to Eq. #5.2.1 we get:
x-(5/2) = √ 81/4
Add 5/2 to both sides to obtain:
x = 5/2 + √ 81/4
Since a square root has two values, one positive and the other negative
x2 - 5x - 14 = 0
has two solutions:
x = 5/2 + √ 81/4
or
x = 5/2 - √ 81/4
Note that √ 81/4 can be written as
√ 81 / √ 4 which is 9 / 2
5.3 Solving x2-5x-14 = 0 by the Quadratic Formula .
A rectangle is drawn with perimeter 75 cm. The length is 13 more than the width. What is the length?
The perimeter of the rectangle is 75 cm, then the length of the rectangle will be equal to 25.25 cm.
What is the perimeter?A shape's perimeter is the whole distance encircling it. It is the perimeter or length of the contour of any geometric two-dimensional shape. The circumference of several figures could be comparable based on the measurements.
As per the information provided by the question,
The perimeter of the rectangle = 75 cm
Let the width of the rectangle is w.
Then, length (l) is 13 more than,
l = w + 13 (i)
As per the formula of the perimeter of a rectangle,
[tex]P=2(l+w)[/tex]
75 = 2(w + 13 + w)
75 = 4w + 26
4w = 49
w = 12.25 cm
Substitute w = 12.25 cm in equation (i)
l = 12.25 + 13
l = 25.25 cm.
To know more about Perimeter:
https://brainly.com/question/6465134
#SPJ5
Which test point holds true for y − 2x ≤ 1?
(0, 2)
(-2, 4)
(1, 4)
(5, 0)
Answer:idek tbh
Step-by-step explanation:
The diagonal of a square is x units. What is the area of the square in terms of x?
square units
square units
2x square units
square units
Let
b------> the length side of a square
we know that
the area of a square is equal to
[tex]A=b^{2}[/tex]
Find the length side of the diagonal applying the Pythagoras Theorem
[tex]d^{2}=b^{2}+b^{2}[/tex]
[tex]d^{2}=2b^{2}[/tex]
[tex]d=b\sqrt{2}\ units[/tex]
Remember that
[tex]d=x\ units[/tex] -----> given problem
substitute
[tex]d=b\sqrt{2}\ units[/tex]
[tex]x=b\sqrt{2}\ units[/tex]
Solve for b
[tex]b=\frac{x\sqrt{2}}{2}\ units[/tex]
Substitute in the formula of area
[tex]A=(\frac{x\sqrt{2}}{2})^{2}[/tex]
[tex]A=\frac{x^{2}}{2}\ units^{2}[/tex]
therefore
the answer is
[tex]\frac{x^{2}}{2}\ units^{2}[/tex]
The area of the square in terms of x is [tex]\( \frac{x^2}{2} \),[/tex] obtained by using the Pythagorean theorem and the formula for the area of a square.
To find the area of the square in terms of [tex]\(x\),[/tex] we need to first understand the relationship between the diagonal and the side length of a square.
In a square, each diagonal divides the square into two congruent right triangles. Using the Pythagorean theorem, we can find the relationship between the diagonal [tex](\(x\))[/tex] and the side length of the square [tex](\(s\)).[/tex]
The Pythagorean theorem states:
[tex]\[ \text{Hypotenuse}^2 = \text{Adjacent side}^2 + \text{Opposite side}^2 \][/tex]
For a square:
[tex]\[ x^2 = s^2 + s^2 \][/tex]
[tex]\[ x^2 = 2s^2 \][/tex]
Now, we can solve for [tex]\(s\)[/tex] in terms of [tex]\(x\):[/tex]
[tex]\[ s^2 = \frac{x^2}{2} \][/tex]
[tex]\[ s = \sqrt{\frac{x^2}{2}} \][/tex]
[tex]\[ s = \frac{x}{\sqrt{2}} \][/tex]
The area [tex](\(A\))[/tex] of a square is given by:
[tex]\[ A = s^2 \][/tex]
Substituting the expression for s in terms of x :
[tex]\[ A = \left(\frac{x}{\sqrt{2}}\right)^2 \][/tex]
[tex]\[ A = \frac{x^2}{2} \][/tex]
Therefore, the area of the square in terms of x is [tex]\( \frac{x^2}{2} \).[/tex]
The question probable may be:
The diagonal of a square is x units. What is the area of the square in terms of x?
When you see a traffic light turn red, you apply the brakes until you come to a stop. Suppose your initial speed was 11.2 m/s, and you come to rest in 34.7 m. How much time does this take? Assume constant deceleration.
...?
To make lemonade, kate uses 1 cup of lemon juice and 2 cups sugar. if she makes a larger amount of lemonade with 10 cups of sugar, how many cups of lemon juice does she need?
Kate uses 1 cup of lemon juice and 2 cups of sugar to make lemonade. She requires 5 cups of lemon juice if she uses 5 cups of sugar to produce a larger batch of lemonade.
What is the ratio?It is defined as the comparison of two quantities to ascertain how many times one yields the other. The ratio can be written as a fraction or as a sign: between two numbers.
It is given that, Kate uses 2 cups of sugar and 1 cup of lemon juice to make lemonade. If she uses 10 cups of sugar to create more lemonade.
The ratio of lemon juice to sugar is 1:2.
For 10 cups of sugar, the number of cups of lemon juice needed as,
We have to maintain the ratio as 1:2.So for 10 cups of sugar, the ratio is maintained as,
=5:10
=1:2
Thus, she needs 5 cups of juice to make lemonade.
Learn more about the ratio here:
brainly.com/question/13419413
#SPJ2
Polygon ABCD is reflected and dilated to give polygon PQRS. The coordinates of the preimage are (2, 2), (6, 8), (12, 8), and (16, 2). The coordinates of the image are (11, 15),
(9, 12), (6, 12), and (4, 15). What is the scale factor of the dilation?
Answer: The scale factor of the dilation is 0.5.
Explanation:
It is given that ABCD is polygon which is reflected and dilated , then we get PQRS.
The vertices of ABCD are (2, 2), (6, 8), (12, 8), and (16, 2) respectively. The vertices of image PQRS are (11, 15),(9, 12), (6, 12), and (4, 15) respectively.
The reflection affects the coordinates but does not affect the length of the sides.
But when we talk about dilation it affects the length of sides according to the scale factor or a constant factor.
If a line segment AB is dilated by scale factor k then length of A'B' is k times length of AB.
[tex]|A'B'|=k\times |AB|[/tex] .... (1)
So we have to find any side length of preimage and the side length of that side in image. it means we have to find AB and PQ.
Use distance formula to find the side length.
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]AB=\sqrt{(8-2)^2+(6-2)^2}=\sqrt{36+16}=2\sqrt{13}[/tex]
[tex]PQ=\sqrt{(9-11)^2+(12-15)^2}=\sqrt{4+9}=\sqrt{13}[/tex]
It is noticed that the size of side in preimage is [tex]2\sqrt{13}[/tex] and the size of same side in image is [tex]\sqrt{13}[/tex].
Using equation (1), we get
[tex]\sqrt{13}=k \times 2\sqrt{13}[/tex]
[tex]k=\frac{1}{2}[/tex]
[tex]k=0.5[/tex]
Hence, the value of scale factor is 0.5.
A building casts a 50-foot shadow. Alex is 5 feet tall and casts a 6-foot shadow. Approximately how tall is the building?
A.24 ft
B.42 ft
C.60 ft
D.50 ft
Answer:
Option B: 42 feet is the answer.
Step-by-step explanation:
The length of the shadow of the building is = 50 feet
Let the height of the building be = L
Height of Alex = 5 feet
Length of Alex's shadow = 6 feet
Now we will equate the ratios.
[tex]\frac{5}{6}= \frac{L}{50}[/tex]
[tex]6L=250[/tex]
[tex]L=250/6[/tex]
L = 41.67 ≈ 42 feet
So, the height of the building is approx 42 feet.
Why do we use decimals in everyday life
What is the factored form of the expression?
s^4 – 16
A. (s - 2)^2(s + 2)^2
B. (s - 2)(s + 2)
C. (s - i)(s + i)(s - 2)(s + 2)
D. (s - 2i)(s + 2i)(s - 2)(s + 2)
15 less than 4 times a number is 9 find the number
What is the value of p in the equation y2=-4x? p=?
Answer:
the value of p=-1
Step-by-step explanation:
General equation of a parabola is
[tex]y^2= 4p(x)[/tex] where vertex is at (0,0)
now we compare the given equation with general form
[tex]y^2=-4x[/tex]
We have -4 in the place of 4p
[tex]4p=-4[/tex]
Divide both sides by 4
so p = -1
the value of p = -1
from 5x^2-6x+8, subtract 3x^2-2x-4?
Franko's pizza is selling their pizzas 35% cheaper than usual. if a pizza normally costs $12.00, how much is it now?
The temperature, in degrees fahrenheit (°
f., decreased at a constant rate from 0°f to -25 °f in 5 hours. by how many degrees did the temperature decrease per hour?
The temperature decreased at a constant rate of 5 degrees Fahrenheit per hour.
Explanation:The question is asking for the rate at which the temperature is decreasing per hour. The temperature started at 0oF and decreased to -25oF. That's a total change in temperature of 25oF (since we're counting how much it dropped below 0o). This change happened over the course of 5 hours. Therefore, to find the rate of change, we divide the total change (25 degrees) by the total time (5 hours). This gives us 5oF per hour. So, the temperature decreased at a rate of 5oF per hour.
Learn more about Rate of Change here:https://brainly.com/question/29181502
#SPJ3