For the dinner special at a restaurant, the customer must choose an appetizer, a salad, an entree, a side dish, and a dessert.Here are the items to choose from.ChoicePossible items Appetizer Buffalo wings, Cheese sticks, Potato skins, Nachos Salad Caesar, Southwest, Garden Entree Lamb, Roast turkey, Salmon, Pot roast, Grilled chicken Side dish Mixed vegetables, Baked potato, Rice, French fries, Corn Dessert Chocolate cake, Brownies, Cheesecake How many dinner specials are possible?
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Solution
Step 1:
There are 4 Appetizers, 3 Salad, 5 Entrees, 5 Side dishes, and 3 Desserts.
Step 2:
Possible dinner special
[tex]\begin{gathered} =\text{ 4 }\times\text{ 3 }\times\text{ 5 }\times\text{ 5 }\times\text{ 3} \\ \\ =\text{ 900 } \end{gathered}[/tex]Final answer
900 specials possible dinner.
900
Related Questions
estimate the answer the amount of money rick spends on gasoline in a year if the average amount he spends per month is $140.87.chose the correct estimate below a: $16,800b:$168 c:2,520d: $1,680
Answers
Given data:
The given amount of money spend in a month is $140.87.
The expression for the given statement is,
[tex]1\text{ month =\$140.87}[/tex]Multiply the above expression by 12 on both sides.
[tex]\begin{gathered} 12(1\text{ month))=12(\$140.87)} \\ 1\text{ year=\$1690.44} \end{gathered}[/tex]Thus, the amount Rick spends in a year is $1690.44.
starting at 00 if you were to go up 7 units and left for you is what coordinates would you end up at what quadrant would you be in
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The coordinate is starting from the origin
7 units up and 4 units to the left
My coordinate will be (4, 7)
This is because the up is positive y- axis and the left is postive x - axis as well
X = 4 and y = 7
Joining the two points together will end up in the first quadrant
The answer is (4, 7) and First quadrant
Use the inverse relationship between logarithmic and exponential functions to solve the equation for x. Simplify your answer using the rules of logarithms and the change of base formula.ln(x) = −2X=________
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using the following property
[tex]e^{b\ln a}=a^b[/tex]We can rewrite our expression by exponentiating both sides:
[tex]\begin{gathered} e^{\ln x}=e^{-2} \\ x^1=e^{-2} \\ x=\frac{1}{e^2} \end{gathered}[/tex]Got a tutor to help but they got the answer wrong and I need help again!
Answers
STATEMENT:
SOLUTION:
ANSWER:
A person’s car uses 4 gal of gasoline to travel 156 mi. He has 3 gal of gasoline in the car, and he wants to know how much more gasoline he will need to drive 300 mi. If we assume that the car continues to use gasoline at the same rate, how many more gallons will he need ?
Answers
The gallons that the person needs more is 4.7 Gallons.
How to calculate the value?Since the person’s car uses 4 gal of gasoline to travel 156 miles, the mile.per gallon will be:
= 156 / 4
= 39 miles per gallon.
Therefore, to travel for 300 miles, the gallons needed will be:
= 300 / 39
= 7.7 gallons
He has 3 gallons, the gallons left will be:
= 7.7 - 3
= 4.7 Gallons
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Line I is parallel to line m. If the measure of >6 is 75^ what is the measure of <4?
Answers
The measure of <4 = 75°
Explanation:Note that:
• <4 and <6 are alternative interior angles
,• Alternative interior angles are equal
Therefore, based on the points given above:
m<4 = m<6 = 75° (Alternative interior angles are equal)
The measure of <4 = 75°
2. Find the measure of ZRST.(5x – 4):R(8x + 4)ºST
Answers
From the picture we notice that the angles R and Q are the same. Furthermore the interior angle S of the triangle is:
[tex]180-(8x+4)[/tex]Then we have the equation:
[tex]2(5x-4)+180-(8x+4)=180[/tex]Solving for x we have:
[tex]\begin{gathered} 10x-8-8x-4=0 \\ 2x-12=0 \\ x=6 \end{gathered}[/tex]Now we plug the value of x in the expression for the angle RST, then:
[tex]8(6)+4=52[/tex]Therefore the angle RST is 52°.
what is the answer to 2(4y-2)=10
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The given equation is expressed as
2(4y-2)=10
graph a right triangle with the two points forming the hypotenuse . using the sides find the distance between two points, to the nearest tenth.(-5,-3) and (4,-1)
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graph a right triangle with the two points forming the hypotenuse . using the sides find the distance between two points, to the nearest tenth.(-5,-3) and (4,-1)
see the attached figure
Find out the distance, using the sides
Applying the Pythagorean Theorem
c^2=a^2+b^2
a=4-(-5)=4+5=9 units
b=-1-(-3)=-1+3=2 units
c^2=9^2+2^2
c^2=81+4
c^2=85
c=√85
c=9.2 unitsWrite a system of equation to this real world situation .Number 1
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Let be "q" the number of quarters Kiara has and "d" the number of dimes she has.
According to the information given in the exercise, the total number of dimes are quarters Kiara has is 100. Based on this, you can set up the following equation, which will be Equation 1:
[tex]q+d=100[/tex]The total value Kiara has is $19, then knowing that 1 quarter is $0.25 and 1 dime is $0.10, you can set up the Equation 2:
[tex]0.25q+0.10d=19[/tex]Then, the System of equation for this situation is:
[tex]\begin{cases}q+d=100 \\ 0.25q+0.10d=19\end{cases}[/tex]The answer is:
- Equation 1:
[tex]q+d=100[/tex]- Equation 2:
[tex]0.25q+0.10d=19[/tex]What is 32/3 as a proper fraction also I am gay if you don't agree don't help and my name is Oliver
Answers
A fraction can be proper or improper.
When a fraction is proper, the numerator is less than the denominator, and therefore, the fraction is less than unity. For example:
[tex]\frac{3}{4}=0.75<1[/tex]When a fraction is improper the numerator is greater than the denominator and therefore the fraction is greater than unity. For example:
[tex]\frac{9}{5}=1.8>1[/tex]So, in this case, you have
[tex]\frac{32}{3}=10.67>1[/tex]Then, as you can see 32/3 is an improper fraction.
To take it to a proper fraction, you can convert this fraction into a mixed number.
A mixed number is made up of an integer part and a proper fraction.
So, you have
[tex]\begin{gathered} \frac{32}{3}=\frac{10\cdot3+2}{3}=\frac{10\cdot3}{3}+\frac{2}{3}=10+\frac{2}{3}=10\frac{2}{3} \\ \text{ Then,} \\ \frac{32}{3}=10\frac{2}{3} \end{gathered}[/tex]Therefore, 32/2 as a proper fraction will be
[tex]10\frac{2}{3}[/tex]A school choir needs to make t-shirts for its 75 members. A printing company charges $2 per shirt, plus a $50 fee for each color to be printed on the shirts. Write an equation that represents the relationship between the number of t- shirts ordered, the number of colors on the shirts and the total cost of the order. If you use a variable (letter) specify what it represents. In this situation, which quantities do you think can vary (change)? Which might be fixed (stay the same)?
Answers
Let's begin by listing out the given information:
total number of members = 75
printing charge = $2 per shirt
colour print for each shirt = $50 fee for each color to be printed on the shirts
Let the number of t-shirts be represented as n
Let the number of colors on the shirts be represented as x
Let the total cost of the order be represented as C
Every member must have a t-shirt means
total number of members * printing charge + (colour print for each shirt * number of colors on the shirts) = total cost of the order
75 * 2 + 50 * x = C
150 + 50x = C
C = 50x + 150
The number of colors on the shirts (x) can vary change; if the number of colors used increases, the cost of the order increases & if the number decreases, the cost of the order decreases
The printing company charges is fixed as every member is to get a shirt
Find an equation of the line that goes through the points (-10,13) and (-4,7). Write your answer in the formY=mx+b
Answers
1) In this problem, let's plug those points into the slope formula to get the slope, i.e. the measure of how steep is the line between those points:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{7-13}{-4-(-10)}=\frac{-6}{6}=-1[/tex]2) Now, let's find the y-intercept, a.k.a. the linear coefficient "b". To do that we need to plug into the Slope-Intercept Formula one of those points, the slope, and solve it for "b"
[tex]\begin{gathered} (-4,7),m=-1 \\ y=mx+b \\ 7=-4(-1)+b \\ 7=4+b \\ 7-4=b \\ b=3 \end{gathered}[/tex]3) Therefore, the equation of the line is:
[tex]y=-x+3[/tex]There are 25 people who work in an office together. Five of these people are selectedto go together to the same conference in Orlando, Florida. How many ways can theychoose this team of five people to go to the conference?
Answers
ANSWER
53,130
EXPLANATION
There are 25 people and 5 have to be chosen from that group, with no specific order,
[tex]_{25}C_5=\frac{25!}{(25-5)!5!}=\frac{25\times24\times23\times22\times21\times20!}{20!\cdot5\times4\times3\times2\times1}=\frac{25\times24\times23\times22\times21}{5\times4\times3\times2\times1}=53,130[/tex]Hence, there are 53,130 ways to choose the five-people team.
Expand (x – 4)^5 using the Binomial Theorem and Pascal’s triangle. Show all necessary steps.
Answers
SOLUTION
The given expression is:
[tex](x-4)^5[/tex]Using binomial theorem, the function is expanded as follows:
[tex](x-4)^5=x^5+5(x)^4(-4)^+\frac{5(5-1)}{2!}x^3(-4)^2+\frac{5(5-1)(5-2)}{3!}x^2(-4)^3+\frac{5(5-1)(5-2)(5-3)}{4!}x^(-4)^4+(-4)^5[/tex]This gives:
[tex](x-4)^5=x^5-20x^4+160x^3-640x^2+1280x-1024[/tex]The pascal triangle is shown:
Using pascal triangle the expansion is shown:
[tex]\begin{gathered} (x-4)^5=x^5+5x^4(-4)+10x^3(-4)^2+10x^2(-4)^3+5x(-4)^4+(-4)^5 \\ (x-4)^5=x^5-20x^4+160x^3-640x^2+1280x-1024 \end{gathered}[/tex]A line passes through(1,-5) and (-3,7) write an equation for the line in point-slope form Rewrite the equation in slope-intercept form A. Y-5=1/3(x+1) ; y =1/3x + 16/3 B. Y+5=-3(x-1); y=-3x-2 C. Y-1=1/3(x+5);y=-1/3x+3/8 D. Y-5=3(x-1);y=3x+8
Answers
Step 1: Concept
Write the formula for the equation of a line in terms of point-slope form
and in slope-intercept form.
[tex]\begin{gathered} Pi\text{ont slope form is given below} \\ y-y_1=m(x-x_1) \\ \text{Slope}-\text{intercept form} \\ y\text{ = mx + c} \\ m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \end{gathered}[/tex]Where
m = slope
c = intercept
Step 2: Represent the coordinates
[tex]\begin{gathered} (x_1,y_1\text{ ) = (1, -5)} \\ (x_2,y_2\text{ ) = ( -3, 7)} \end{gathered}[/tex]Step 3: Find the slope, using slope formula.
[tex]\begin{gathered} m\text{ = slope} \\ \text{m = }\frac{y_2-y_1}{x_2-x_1} \\ m\text{ = }\frac{7\text{ -(-5)}}{-3\text{ -1}} \\ m\text{ = }\frac{7\text{ + 5}}{-4} \\ m\text{ = }\frac{12}{-4} \\ m\text{ = -3} \end{gathered}[/tex]Step 4: Write an equation for the line in point-slope form.
[tex]\begin{gathered} \text{y - y}_1=m(x-x_1) \\ y\text{ -(-5) = -3(x - 1)} \\ \text{y + 5 = -3(x - 1)} \end{gathered}[/tex]Step 5: Simplify the equation in 4 to write the equation in slope-intercept form.
y + 5 = -3(x - 1)
y + 5 = -3x + 3
y = -3x + 3 - 5
y = -3x - 2
Final answer
Option B
y + 5 = -3(x - 1)
y = -3x - 2
Explain the different ways a linear equation can be transformed. Then give an example and describe the transformation. (It's not a Test, I don't know how to explain that's why)
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Answer: Translation, Rotation, or Reflection
Step-by-step explanation: The graphs of linear functions can be transformed without changing the shape of the line by changing the location of the y-intercept or the slope of the line. Those lines can be transformed by translation, rotation, or reflection, and still follow the slope-intercept form y = MX + b
Which of the following equations is the translation 2 units down of the graph of y = Ixl?y = |x - 2|y = |x + 2|y = |xl - 2y = Ixl + 2
Answers
Answer:
y = | x | - 2
Explanation:
If we have a function g(x) = f(x) + c, we can say that g(x) is a translation of c units up or down of f(x)
If c is negative, the translation is c units down.
Therefore, the translation of 2 units down of the graph y = | x | is:
y = | x | - 2
A standard deck of cards has 52 cards. Suppose you decide to play a game using only half of a standard deck. If you draw one card at a time from the half-deck, without replacement, how many different ways can you draw all of the cards? Remember that "without replacement" means that the cards are not returned to the deck after they are chosen. Write your answer in factorial notation.
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We are asked to determine in how many ways we can draw all of the cards in half a deck. Since in a deck there are 52 cards, in half a deck there are:
[tex]n=\frac{52}{2}=26[/tex]The number of ways in which the cards can be drawn is equivalent to the number of permutations. And this is equivalent to:
[tex]P=n![/tex]Where "p" is the number of permutations and n! is the factorial of the number of cards in half a deck. Substituting the values we get:
[tex]P=26![/tex]Solving the operations:
[tex]P=403291461126605635584000000[/tex]Thus we determine the number of ways the cards can be drawn.
Enter the ordered pair for the vertices for (90, (QRST).уQ-RoSRQ=R'=(S'=T=(
Answers
Let P(h,k) be the coordinates of a point in the figure. When the figure is rotated 90 degree about the origin in clockwise direction, the new coordinates become P'(k,-h).
Therefore,
Q(1,3)--->Q'(3,-1)
R(3,-3)--->R'(3,-3)
S(0,2)---->S'(2,0)
T(-2,1)---->T'(1,2)
Kim bought new shoes and used a 12% off coupon. The original cost of the shoe is represented as s. The total amount Kim paid for the shoes is represented as s-0.12s= s, which means that _______ of 12% is the same as ___
Answers
The difference s - 0.12s is equal to 0.88s. So, the first blank has to be 0.88.
The second blank is "decrease", and the last one is "multiplying by 0.88" because the difference is actually equivalent to 0.88s.
Given a function f(x)=|7-4x| ,find the objects with an image 11
Answers
Given the function f(x) defined as:
[tex]f(x)=|7-4x|[/tex]If the image is 11, the corresponding objects (x-values) are:
[tex]\begin{gathered} |7-4x|=11 \\ 7-4x=11\ldots(1) \\ 7-4x=-11\ldots(2) \end{gathered}[/tex]Solving (1) to find the first object:
[tex]\begin{gathered} 7-4x=11 \\ 7-11=4x \\ -4=4x \\ x=-1 \end{gathered}[/tex]Now, we solve (2) to find the second object:
[tex]\begin{gathered} 7-4x=-11 \\ 7+11=4x \\ 18=4x \\ x=4.5 \end{gathered}[/tex]Answer: -1 and 4.5
On a school trip, there are 9 boys, 10 girls and 4 adults. Write each as a ratio.Girls to Boys10:9Boys and Girls to Adults9:10:4Adults to Boys and Girls4:9:10
Answers
Given
Boys = 9
Girls = 10
Adults = 4
Find
ratio
Explanation
girls to boys
as girls are 10 and boys are 9 ,
so the ratio =
[tex]10\colon9[/tex]boys and girls to adults
boys and girls = 9 + 10 = 19
so the ratio =
[tex]19\colon4[/tex]adults to boys and girls
[tex]4\colon19[/tex]Final Answer
a) 10:9
b) 19:4
c) 4:19
The isotope Sr-85 is used in bone scans. It has a half-life of 64.9 days. If you start with a10-mg Sample, how much would be remaining after 50 days? Round to the nearest hundredth.
Answers
The formula for the half life is as follows:
[tex]N(t)=N_0\mleft(\frac{1}{2}\mright)^{\frac{t}{(t_{_{_{1)}}}}}[/tex]where N(t) is the final amount, N₀ is the initial amount, t is the time that passed, and t2 is the half-life.
The following are the given values in the problem:
[tex]\begin{gathered} N_0=10 \\ t=50 \\ t2=64.9_{} \end{gathered}[/tex]Substitute the values into the equation.
[tex]N(50)=10\mleft(\frac{1}{2}\mright)^{\frac{50}{64.9}}[/tex]Simplify the right side of the equation. Divide 50 by 64.9 and then raise 1/2 by the obtained quotient. And finally, multiply the obtained value by 10.
[tex]\begin{gathered} N(50)\approx10\mleft(\frac{1}{2}\mright)^{0.7704160247} \\ \approx10(0.5862483959) \\ \approx5.862483959 \end{gathered}[/tex]Therefore, after 50 days, it will become approximately 5.86 mg.
7.) Write the equations below in words m=2×7÷9
Answers
Given
[tex]m=2\cdot\frac{7}{9}[/tex]
Procedure
m is equal to the multiplication of 2 by 7 and then divided by 9.
2. Microsoft Corp. has made an offer to acquire 1.5 million shares of Apple$374 per share. They offered Apple 10 million shares of Microsoft worth $25 pershare, but they need to make up the difference with other shares. They have othershares worth $28 per share. How many of the $28 shares (to the nearest share) dothey also have to offer to make an even swap? Explain your work using words,numbers, and/or pictures
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If f(x) =(if necessary)?(x-76what is the value of f(3), to the nearest thousandth
Answers
The function we have is:
[tex]f(x)=\frac{\sqrt[]{x}-7}{6}[/tex]And we need to find the value of f(3).
To solve this problem and find f(x), we need to substitute x=3 into the given function.
• Substituting x=3 into f(x) to find f(3):
[tex]f(3)=\frac{\sqrt[]{3}-7}{6}[/tex]And now, we start solving the operations.
Since the square root of 3 is equal to 1.732:
[tex]f(3)=\frac{1.732-7}{6}[/tex]Substracting 7:
[tex]f(3)=\frac{-5.268}{6}[/tex]And finally, dividing by 6:
[tex]f(3)=-0.878[/tex]To round to the nearest thousandth we need to round to 3 decimal places, which in this case we already have, thus, the final answer is:
[tex]-0.878[/tex]10. Do the ratios -2:1,-4: 2 and - 6:3 represent a proportional relationship? O No, the ratios do not represent a proportional relationship because, when graphed, the line passes through the origin but is not straight. No, the ratios do not represent a proportional relationship because, when graphed, the line is not straight, and it does pass through the origin. Yes, the ratios represent a proportional relationship because, when graphed, the line passes through the origin and is a straight line. No, the ratios do not represent a proportional relationship because, when graphed, the line is straight, but it does not pass through the origin.
Answers
Solution
For this case we have the following proportions:
-2:1 = -2
-4:2 = -2
-6:3 = -2
If we plot the relationship we got something like this
And then we can conclude that the answer is:
Yes the ratios represent a proportional relationship because when graphed the line passes through the origin and is a straight line
in general the ____ of a linear model represents how the two types of data change in correlation of each other.1. trend line2. y-intercept3. slope4. x intercept5. correlation coefficient
Answers
How 2 tipes of data change
it could be two options
Trend line
Coefficient of correlation
Write a compound inequality for the graph shown below.Use x for your variable.++-10-9-8-7 -6 -5 4-3-2-1002 3 4 5 6 7 8 9 10 xDand口口>DorOSONO?X
Answers
The question said we should write a compound inequality of the given graph.
We are also asked to use x as the variable.
From the graph, we can see that both end values are shaded dots, which means x is inclusive of those two values.
Since:
x ≥ -5
and
x ≤ 6
Therefore, the compound inequality of the given graph is:
-5 ≤ x ≤ 6.