Last week a pizza restaurant sold 36 cheese pizzas, 64 pepperoni pizzas, and 20 veggie pizzas. Based on these data, what is the probability that the next customer will buy a cheese pizza? Determine the likelihood of this event.
Supposing the same rates, the likelihood of a customer choose a cheese pizza can be calculated by the number of times cheese pizzas were chosen divided by the total of pizzas, so:
[tex]P=\frac{36}{36+64+20}=\frac{36}{120}=\frac{3}{10}[/tex]So, the lokelihood of this event is 3/10, or 30%.
how do you solve for x in the following problem... 23 + 6x = 29
The expression we have to solve for x is:
[tex]23+6x=29[/tex]In any given equation, to solve for a variables we need to leave that variable alone in one side of the equation.
In this case we need to get rid of the 23 that is besides the 6x on the left side.
For that:
Step 1. Substract 23 from both sides of the equation:
[tex]23-23+6x=29-23[/tex]23-23 in the left side cancel each other. And we are left with:
[tex]6x=29-23[/tex]since 29-23 is equal to 6:
[tex]6x=6[/tex]Step 2. Divide both sides of the equation by 6:
[tex]\frac{6x}{6}=\frac{6}{6}[/tex]and since 6/6=1 we are left with the following result:
[tex]\begin{gathered} x=\frac{6}{6} \\ \\ x=1 \end{gathered}[/tex]Answer: x = 1
Find the measure ZBCD in thefollowing parallelogram.ADХ2xх2xBCmZBCD = [ ? 10Enter
x + x + 2x + 2x = 360°
Then
6x = 360°
x = 360/6 = 60°
∠BCD = 2X = 2*60 = 120°
5
Boxes of pencils cost $2.50 each, including tax. Alex spent a
total of $55 on pencils. Write and solve an equation to
determine how many boxes of pencils Alex bought.
(variables, numbers, and operations)
=
(total)
The equation can be given as [tex]2.5x=55[/tex] and Alex bought [tex]22[/tex] number of boxes
What is linear equation in one variable?
A linear equation is a equation in one variable whose degree is one.
We are given that Alex bought boxes of pencils worth $55 and the cost of 5 boxes of pencils is $2.5 each
Let the number of boxes of pencils bought by Alex is [tex]x[/tex]
Therefore the equation can be given as,
[tex]2.5x=55[/tex]
Dividing both sides by 2.5,
[tex]x=22[/tex]
Therefore, The equation can be given as 2.5x=55 and Alex bought 22 boxes of pencils
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What is familiar about this situation? (3²)(3²) (3²)(3²)
Answer:
they are repetative situations
Step-by-step explanation:
If BC = 5x - 9 and AB = 2x + 21, find the value of x.
Suppose that B is the midpoint of segment AC; therefore, AB=BC
Thus,
[tex]\begin{gathered} AB=BC \\ \Rightarrow2x+21=5x-9 \end{gathered}[/tex]Solve for x as shown below
[tex]\begin{gathered} \Rightarrow3x-9=21 \\ \Rightarrow3x=30 \\ \Rightarrow x=10 \end{gathered}[/tex]Therefore, the answer is x=104x3 + 0x2 – 3x - +4 2x - 5 What will the first row of this multiplication be? 0-2013 -20x3 - 5x2 + 15% - 20 423 + 0x2 - 6x 6x - 20 O 423 + 0x2 - 12 - 1 - 20x3 + 0x2 + 152 – 20
Answer:
[tex]-20x^3+0x^2+15x-20[/tex]Explanation:
Step 1. To find the first row of the multiplication, we need to multiply -5 by the first expression:
[tex]4x^3+0x^2-3x+4[/tex]The multiplication we have to make is:
[tex](-5)(4x^3+0x^2-3x+4)[/tex]Step 2. Multiply -5 by all of the terms in the expression:
[tex]=(-5)(4x^3)+(-5)(0x^2)+(-5)(-3x)+(-5)(4)[/tex]Solving the operations:
[tex]-20x^3+0x^2+15x-20[/tex]This is the first row of the multiplication and is shown in the fourth option.
Answer:
[tex]-20x^3+0x^2+15x-20[/tex]A single, six sided die is rolled. Find the probability of rolling an odd number or a number less than 4
SOLUTION
The odd numbers in a six sided die are 1, 3 and 5. That is 3 numbers
The numbers less than four are 1, 2 and 3. That is 3 numbers
The probability of rolling an odd number becomes
[tex]\begin{gathered} Pr(odd)=\frac{3}{6} \\ =\frac{1}{2} \end{gathered}[/tex]Probability of rolling a number less than 4 becomes
[tex]\begin{gathered} Pr(less\text{ than 4\rparen = }\frac{3}{6} \\ =\frac{1}{2} \end{gathered}[/tex]Now looking at the odd numbers and the numbers less 4, we have
1, 3, 5 and 1, 2, 3. So between these numbers are 1 and 3. which is 2. Probability of this is
[tex]\begin{gathered} =\frac{2}{6} \\ =\frac{1}{3} \end{gathered}[/tex]Hence the probability of rolling an odd number or a number less than 4 becomes
[tex]\begin{gathered} \frac{1}{2}+\frac{1}{2}-\frac{1}{3} \\ \frac{3+3-2}{6} \\ =\frac{4}{6} \\ =\frac{2}{3} \end{gathered}[/tex]Hence the answer is 2/3
The length of the banner is 3 times its width. The area of the whole banner is 75 square feet. What is the banner’s width and length in feet?
times this number 5x3 15 then this 3x70 you get this 210 add them up 225feet
Draw an angle with the given measure in standard position. 5x180 4711 degreessadons x 6) ST 5) 4 18 y degrees=-414 degrecse-490 4 = 5x45 ==225 13 Das
Answer:
and
Step by step explanation:
An angle is in standard position if its vertex is located at the origin, and its initial side extends along the positive x-axis.
6. Given WY with W(3, 7) and Y(13, -8), if Xpartitions WY such that the ratio of WX to XYis 3:2, find the coordinates of X.
Answer:
(9, -2)
Explanation:
If a point X partition a segment that starts in point (x1, y1) and ends at point (x2, y2) in a ration a:b, the coordinates of X will be equal to:
[tex](\frac{a}{a+b}(x_2-x_1)+x_1,\frac{a}{a+b}(y_2-y_1)+y_1)[/tex]So, replacing (x1, y1) by point W(3, 7) and (x2, y2) by point Y(13, -8) and the ratio a : b by 3 : 2, we get that the coordinates of X are:
[tex]\begin{gathered} (\frac{3}{3+2}(13-3)+3,\frac{3}{3+2}(-8-7)) \\ (\frac{3}{5}(10)+3,\frac{3}{5}(-15)+7) \\ (6+3,-9+7) \\ (9,-2) \end{gathered}[/tex]Therefore, the coordinates of X are (9, -2)
Find the slope of the line that goes through the given points.
(-8, 7), (-8, 6)
Group of answer choices
16
0
- (16/13)
Answer:
0 or undefined
Step-by-step explanation:
Hey! Let's help you with your question here!
So, you're trying to find the slope of a line that goes through two given points. To recall, we're trying to find m from the slope-intercept form ([tex]y=mx+b[/tex]). Now we have two points, so is it possible to find the slope given that? Yes! It is! And that is using the slope between two points! Here's how it works:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
This is the formula! Essentially, we'll be able to figure out the slope based on two points in just plugging in the x and y coordinates into the formula. So it becomes:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{6-7}{-8-(-8)}[/tex]
[tex]m=\frac{-1}{0}[/tex]
Now, a problem arises here. While the numerator does give us a value of -1, the denominator ends up being a value of 0. We cannot divide anything by 0 because there's nothing to divide -1 into. In this case, the slope of this line would be classified as undefined. However, in the case of your answer choices, if we were to plot the points on the graph, you'll notice that it's a vertical straight line. So the slope would technically 0.
Answer 54 side a and b like side a answer for 1 is … and so on
Addition of fraction:
1. 13/18 7. 7/8
2. 19/28 8. 29/36
3. 29/24 9. 23/60
4. 1/2 10. 1/2
5. 47/40 11. 11/56
6. 37/36 12. 13/45
Given, the expressions are:
1. 1/6 + 5/9
take LCM of 6 and 9
LCM = 18
hence, 1×3/6×3 + 5×2/9×2
= 3/18+10/18
= 3+10/18
= 13/18
2. 1/4 + 3/7
take LCM of 4 and 7
LCM = 28
hence, 1×7/4×7 + 3×4/7×4
= 7/28+12/28
= 7+12/28
= 19/28
3. 5/6+3/8
take LCM of 6 and 8
LCM = 24
hence, 5×4/6×4 + 3×3/8×3
= 20/24+9/24
= 20+9/24
= 29/24
4. 2/5+1/10
take LCM of 5 and 10
LCM = 10
hence, 2×2/5×2 + 1×1/10×1
= 4/10+1/10
= 4+1/10
= 5/10
= 1/2
5. 7/8 + 3/10
take LCM of 8 and 10
LCM = 40
hence, 7×5/8×5 + 3×4/10×4
= 35/40+12/40
= 35+12/40
= 47/40
6. 4/9+7/12
take LCM of 9 and 12
LCM = 36
hence, 4×4/9×4 + 7×3/12×3
= 16/36+21/36
= 16+21/36
= 37/36
7. 1/4+5/8
take LCM of 4 and 8
LCM = 8
hence, 1×2/4×2 + 5×1/8×1
= 2/8+5/8
= 2+5/8
= 7/8
8. 1/4+5/9
take LCM of 4 and 9
LCM = 36
hence, 1×9/4×9 + 5×4/9×4
= 9/36+20/36
= 9+20/36
= 29/36
9. 3/10+1/12
take LCM of 10 and 12
LCM = 60
hence, 3×6/10×6 + 1×5/12×5
= 18/60+5/60
= 18+5/60
= 23/60
10. 2/7+3/14
take LCM of 7 and 14
LCM = 14
hence, 2×2/7×2 + 3×1/14×1
= 4/14+3/14
= 4+3/14
= 7/14
= 1/2
11. 1/8+1/14
take LCM of 8 and 14
LCM = 56
hence, 1×7/8×7 + 1×4/14×4
= 7/56+4/56
= 7+4/56
= 11/56
12. 2/9+1/15
take LCM of 9 and 15
LCM = 45
hence, 2×5/9×5 + 1×3/15×3
= 10/45+3/45
= 10+3/45
= 13/45
Hence we get the desired answers of the fractions in addition form.
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write an equation of the line in slope intercept form given the following information: slope: 3, through (2, 5)
we already have the slope so in this case we can use the equation of the slope and replace its values, ane coordinate (2,5) and replace x=0 so:
[tex]\begin{gathered} m=\frac{y-y_1}{x-x_1} \\ 3=\frac{y-5}{0-2} \end{gathered}[/tex]and we solve for y so:
[tex]\begin{gathered} -2\cdot3=y-5 \\ -6+5=y \\ -1=y \end{gathered}[/tex]So the equation is:
[tex]y=3x-1[/tex]The Brady family received 31 pieces of mail on January 28. The mail consisted of bills,letters, and magazines. How many bills did they receive if they received three more letters than ads, the same number of bills as ads, and five more magazines than letters.
The Solution.
Let the number of ads be = x
Number of Letters = x+3
Number of bills = x
Number of magazines = x+3+5 = x+8
Given that the total number of mail is 31, we have
[tex]x+x+3+x+x+8=31[/tex]Collecting the like terms, we get
[tex]\begin{gathered} x+x+x+x+11=31 \\ 4x=31-11 \\ 4x=20 \\ \text{Dividing both sides by 4, we get} \\ x=\frac{20}{4}=5 \end{gathered}[/tex]So, the number of bills they received is 5.
Hence, the correct answer is 5 bills.
Find the sum of 3 and -3
Answer:
Given:
[tex]3+(-3)=\text{?}[/tex]The sum of given two number is,
[tex]3+(-3)=3-3=0[/tex]So, the answer is zero.
44° 6 Find the value of x to the nearest tenth.
Given:
Angle = 44 degrees.
Adjacent side = 6 units.
Hypoteuse side = x units
Recall the formula for cosine,
[tex]\cos \theta=\frac{Adjacent\text{ side}}{\text{Hypoteuse side}}[/tex]Substitute Adjacent side = 6 units, Hypoteuse side =x units and angle =44, we get
[tex]\cos 44^o=\frac{6}{x}^{}[/tex][tex]\text{ Use }\cos 44^o=0.719.[/tex][tex]0.179=\frac{6}{x}^{}[/tex][tex]x=\frac{6}{0.179}[/tex][tex]x=8.34[/tex]Round off, we get
[tex]x=8.3\text{ units}[/tex]Hence the value of x is 8.3 units.
help is need 50 points
Answer: 32s-24
Step-by-step explanation:
Multiply each term in parentheses by 6, combine like terms
Answer:
32s-24
Step-by-step explanation:
The shaded part of the diagram shows the top of a stove.
What is the area of the stove top?
The area of the stove top is 7 ft².
What is meant by area?
The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.
Area equals length times width.
Area = l b. Area = r2( = 3.14), where r is the radius. These methods can also be used to determine the area of various quadrilaterals, a particular type of polygon with four sides and angles less than 90 degrees.
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.
Given ,
Length = 3 1/2
Width = 2ft
Area=3 1/2*2
= 7/2*2
= 7ft²
Therefore the area of the stove top is 7ft²
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Find the GCF (greatest common factor) of the following terms.{4xy^2, 2x^2y^2, x^2y^2}
We need to find the GCF of
[tex]\begin{gathered} 4xy^2 \\ 2x^2y^2 \\ \text{and} \\ x^2y^2 \end{gathered}[/tex]Let's break apart the terms,
[tex]\begin{gathered} 4xy^2=2\cdot2\cdot x\cdot y\cdot y \\ 2x^2y^2=2\cdot x\cdot x\cdot y\cdot y \\ x^2y^2=x\cdot x\cdot y\cdot y \end{gathered}[/tex]We can see that the common factors to all 3 terms are x * y * y, which
[tex]\begin{gathered} x\cdot y\cdot y \\ =xy^2 \end{gathered}[/tex]Thus, the GCF of the 3 terms given is,
[tex]xy^2[/tex]Answer[tex]xy^2[/tex]Colby put $100 in a savings account. The graph below shows how the amount in the
account would increase over the next ten years. y=mx
a) Write the equation of the line.
b) What does the y-intercept represent?
c) Interpret the slope.
Jevonte is saving money. Jevonte started with $21 and added $17.50 every week. Find the rate of change.
The rate of change is $17.5 per week.
A rate in mathematics is the comparison of two related values expressed in different units.
The numerator of the ratio indicates the rate of change in the other (dependent) variable if the denominator of the ratio is written as a single unit of one of these quantities, and if it is assumed that this quantity may be modified systematically (i.e., is an independent variable). When viewed broadly, a rate (or ratio) can be conceived of as an output-input ratio or a benefit-cost ratio. For instance, in the transportation industry, miles per hour is the output (or benefit) in terms of miles of travel that one receives from travelling for one hour (a cost in time) (at this velocity).Jevonte adds $17.50 every week. so the rate of change in his account each week is 17.5 dollars.
Therefore the rate of change is 17.5 dollars per week.
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Identify the vertex, axis of symmetry, and min/max value of each.
we have the function
f(x)=3x^2-54x+241
this is a vertical parabola open upward (because the leading coefficient is positive)
the vertex is a minimum
Convert the quadratic equation into vertex form
y=a(x-h)^2+k
where
(h,k) is the vertex
and the axis of symmetry is equal to the x-coordinate of the vertex
so
x=h
step 1
Factor the leading coefficient
[tex]\begin{gathered} f(x)=3(x^2-18x)+241 \\ \text{complete the squares} \\ f(x)=3(x^2-18x+9^2-9^2)+241 \\ f(x)=3(x^2-18x+9^2)+241-(9^2)\cdot(3) \\ f(x)=3(x^2-18x+81)+241-243 \\ \text{rewrite as p}\operatorname{erf}ect\text{ squares} \\ f(x)=3(x-9)^2-2 \end{gathered}[/tex]the vertex is the point (9,-2)the axis of symmetry is x=9the vertex represent a minimum23.Find the constant rate of change in the value of Car A and in the value of Car B after theinitial depreciation.24.Based on the data in the table and the constant rate of changes for each vehicle, write anequation to predict the value of Car A and Car B at the end of t years
For Car A:
Initial depreciation = 30000(0.25)
= 7500
Cost = 30000 - 7500
= $22500
Equation = Cost = $22500 - 2000t This is the equation for Car A
For Car B
Initial depreciation = 25000(0.1)
= 2500
Cost = 25000 - 2500 = 22500
Equation Cost = 22500 - 1500t This is the equation for Car B
Question 6 of 13Question 6 (1 point)Find the measure(s) of the exterior angle(s) of the polygon.34°XtoThe measure of the missing exterior angles of the polygon are degrees anddegrees.
The sum of exterior angles of a polygon is 360⁰
There are four exterior angles in the given polygon or quadrilateral which sum up to 360⁰
Hence,
[tex]\begin{gathered} x^0+x^0+34+90=360^0 \\ 2x^0+124^0=360^0 \\ 2x^0=236^0 \\ x=\frac{236}{2} \\ x=118^0 \end{gathered}[/tex]Therefore, the measure of the missing exterior angles of the polygon are 118 degrees and 118 degrees
In 1855, a person sold a house to a lady for $28. If the lady had put the $28 into a bank account paying 4% interest, how much would the
investment have been worth in the year 2010 if interest were compounded in the following ways?
a. monthly
b. continuously
a. If compounded monthly, the investment would be worth $ in 2010.
(Round to the nearest dollar as needed.)
The most appropriate choice for compound interest will be given by-
1) If compounded monthly, amount = $9160
2)If compounded continuously, amount = $218
What is compound interest?
If the interest on a certain principal at a certain rate over a certain period of time increases exponentially (not linearly), the interest earned is known as compound interest.
If P is the principal, r is the rate and t is the time in years,
[tex]A = P(1+\frac{r}{100})^n[/tex]
Here,
Principal = $28
Rate = 4%
Time = 2010 - 1855
= 145 years
a) If compounded monthly
Amount =
[tex]28(1 + \frac{4}{1200})^{145\times 12}\\28(1 + \frac{1}{300})^{1740}\\28(\frac{300+1}{300})^{1740}\\28(\frac{301}{300})^{1740}\\28 \times 327.13\\[/tex]
$9159.56
$9160
b) If compounded continuously
Amount =
[tex]28 \times e^{4\times 145}\\28e^{580}\\28 \times 7.78\\[/tex]
$217.84
$218
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How many different ways can a senior project manager and an associate project manager and a technician be selected for an analytics project if there are eleven data scientists available?
The number of different ways that a senior project manager and an associate project manager and a technician can be selected for an analytics project if there are eleven data scientists available is; 990 ways
How to carry out Permutations?
When we pick a particular set of objects in order, it means that we are constructing a permutation. The number of permutations that can be constructed in this way is defined as the product of the number of ways that each object in the given set can be selected.
The formula for permutation is;
P(n,r) = n!/(n-r)!
Thus, different ways can a senior project manager and an associate project manager and a technician be selected for an analytics project if there are eleven data scientists available is;
P(11, 3) = 11!/(11 - 3)!
= 990 ways
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2x + 8 = 6 need help
The given expression is
[tex]2x+8=6[/tex]First, we subtract 8 from each side
[tex]\begin{gathered} 2x+8-8=6-8 \\ 2x=-2 \end{gathered}[/tex]Then, we divide the equation by 2.
[tex]\begin{gathered} \frac{2x}{2}=-\frac{2}{2} \\ x=-1 \end{gathered}[/tex]Hence, the solution is x = -1.Answer:
x=-1
Step-by-step explanation:
2x+8=6
-8. -8
2x=-2
/2. /2
X=-1
what is the function g(x) that results when translating the function f(x)=|x| to the left 12 units and reflecting it over the x-axis?
The function g(x) that results when translating the function f(x) = |x| to the left 12 units and reflecting it over the x-axis is; g(x) = -|x + 12|
What is the translation of the function?
We are given the function as; f(x) = |x|
Now, we are told that it is first translated tp the left by 12 units. Now, it is pertinent to note that when we translate a function by a units to the left it means that we add a units to the x value.
Thus, a translation of f(x) by 12 units to the left gives us;
f'(x) = |x + 12|
Now, we are told that the next transformation is reflection over the x-axis. When we reflect over the x-axis, it means a negative of the function which means we now have;
g(x) = -|x + 12|
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A woman can bicycle 60 miles in the same time as it takes her to walk 18 miles. She can ride 7 mph faster
than she can walk. How fast can she walk?
She can walk how many mph
Answer:
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