Given
Cost of 1 bag of popcorn=$5.50
Cost of 1 drink=$4
Required
we need to find how much would it cost for for 4 bags of popcorn and 6 drinks.
we also need to find how much would it cost for p number of bags and d drinks.
Explanation
Here
cost of 1 bag of popcorn=$5.50
so cost of 4 bags of popcorn=
[tex]5.50\times4=22\text{ dollars}[/tex]Now cost of 1 drink=$4
so cost of 6 drinks=
[tex]6\times4=24\text{ dollars}[/tex]Now cost of 4 bags of popcorn and 6 drinks=22+24=$46
Also cost of p bags of popcorn=5.50p
cost of d drinks=4d
so cost of p bags of popcorn and d drinks=$(5.50p+4d).
Is the function increasing or decreasing over its entire domain?Choose the correct answer below.OA. increasingOB. constantOC. decreasing
Given the following function:
[tex]\text{ f\lparen x\rparen= a}^{\text{x}}[/tex]At a < 1, the function is decreasing
At a > 1, the function is increasing
Therefore, the answer is CHOICE A.
How do you solve letter b using a subtraction equation with one variable that has a solution of 2/3
Let x be the variable. Then, a subtraction equation which involves the variable x and 2/3 as a result could be:
[tex]x-\frac{1}{3}=\frac{1}{3}[/tex]because, x wil be given as
[tex]\begin{gathered} x=\frac{1}{3}+\frac{1}{3} \\ x=\frac{2}{3} \end{gathered}[/tex]I need help with my mathCheck whether (0, 0) is a solution(1) x > -4
ANSWER
Yes, (0,0) is a solution.
EXPLANATION
To check if (0,0) is a solution of this inequality we simply have to replace x by 0 and y by 0. If the inequality is true after replacing, then the point is a solution.
In this inequality we only have x,
[tex]0>-4[/tex]0 is indeed greater than -4, thus this inequality is true and therefore (0, 0) is a solution
4) Find the missing sides of the triangle. Leave your answersas simplified radicals. (2 points)45°2√645°
Remember that
In a 45-90-45 degrees right triangle
The legs are equal
so
The length of the horizontal leg is 2√6 units
Find out the length of the hypotenuse
Applying the Pythagorean Theorem
[tex]\begin{gathered} c^2=(2\sqrt{6})^2+(2\sqrt{6})^2 \\ c^2=24+24 \\ c^2=48 \\ c=4\sqrt{3} \end{gathered}[/tex]therefore
The missing sides of the triangle are
2√6 and 4√3The diagram shows a tin can in the shape of a cylinder and its dimensions. What is the volume of the can in cubic inches in terms of tt? А 1087 in. B 3241 in. 9 in. 3 © 817 in. D 541 in. 6 in. -
The volume of a cylinder is:
[tex]V=\pi r^2h[/tex]Where:
r is the radius
h is the height
You have the diameter on the base, you use the diameter to find the radius, as the diameter is:
[tex]d=2r[/tex]Then, the radius is:
[tex]r=\frac{d}{2}[/tex]d=6in
[tex]r=\frac{6in}{2}=3in[/tex]Then, the volumen of the given cylinder is: 81pi cubic inches[tex]V=\pi(3in)^2\cdot9in[/tex][tex]V=\pi\cdot9in^2\cdot9in[/tex][tex]V=81\pi in^3[/tex]A store offers a discount of $57 whenyou buy a painting with an originalprice of $100.What is the percent discount?
Given:
Discount offered = $57
Original price of paint = $100
Let x represent the percentage discount.
Thus, we have:
x% of $100 = $57
Solving further, we have:
[tex]\frac{x}{100}\ast100=57[/tex][tex]\begin{gathered} \frac{100x}{100}=57 \\ \\ x\text{ = 57\%} \end{gathered}[/tex]Therefore, the percentage discount is 57%
ANSWER:
57%
what is the total cost of a $716 tablet computer that is on sale at 15% off if the local sales tax rate is 7%, the cost of the tablet is how much money round to two decimal places as needed
Since the cost of the tablet is $716
Since the discount on it is 15%
Then let us find the cost after the discount
Multiply 15% by 716 to find the amount of the discount, then subtract it from the cost
[tex]\begin{gathered} d=\frac{15}{100}\times716 \\ d=107.4 \end{gathered}[/tex]Now, find the cost after the discount
[tex]\begin{gathered} C=716-107.4 \\ C=608.6 \end{gathered}[/tex]Let us find the cost after adding 7% for tax
The cost after the tax will be 100% + 7% = 107%
Then multiply 107% by $608.6 to find the final cost
[tex]\begin{gathered} FC=\frac{107}{100}\times608.6 \\ FC=651.202 \end{gathered}[/tex]Round it to 2 decimal places, then
FC = $651.20
The final cost of the tablet is $651.20
Find the answer for given questions? Slope- intercept? Point slope standard form?
Answer:
The equation in slope-intercept form will be;
[tex]y=-\frac{1}{2}x+1[/tex]The function in point-slope form is;
[tex]y-2=-\frac{1}{2}(x+2)_{}[/tex]The standard form of the equation is;
[tex]x+2y=2[/tex]Explanation:
Given the function f(x);
[tex]\begin{gathered} f(-2)=2 \\ f(8)=-3 \end{gathered}[/tex]Firstly, let us find the slope;
[tex]\begin{gathered} m=\frac{f(8)-f(-2)}{8-(-2)}=\frac{-3-2}{8+2}=\frac{-5}{10} \\ m=-\frac{1}{2} \end{gathered}[/tex]we can then solve for the constant term;
[tex]\begin{gathered} y=mx+b \\ at\text{ f(-2)=2;} \\ 2=-\frac{1}{2}(-2)+b \\ 2=1+b \\ b=2-1 \\ b=1 \end{gathered}[/tex]The equation in slope-intercept form will be;
[tex]y=-\frac{1}{2}x+1[/tex]Applying the point-slope form of equation;
[tex]y-y_2=m(x-x_2)[/tex]Substituting the second point;
[tex]\begin{gathered} y-2=-\frac{1}{2}(x-(-2)) \\ y-2=-\frac{1}{2}(x+2)_{} \end{gathered}[/tex]The function in point-slope form is;
[tex]y-2=-\frac{1}{2}(x+2)_{}[/tex]The standard form of the equation can be written as;
[tex]\begin{gathered} y=-\frac{1}{2}x+1 \\ \frac{1}{2}x+y=1 \\ \text{multiply through by 2} \\ x+2y=2 \end{gathered}[/tex]The standard form of the equation is;
[tex]x+2y=2[/tex]elimination Strategy
-2x -4y = 38
5x - 4y = 3
To eliminate, since the coefficient of y is the same, we need to eliminate y by subtracting
So the correct option is A
The shaded area in the circle below represents a damaged section of a 6-foot diameter tabletop.What value is closest to the area of the damaged section?A. 4.0 square feetB. 8.1 square feetC. 7.7 square feetD. 6.0 square feet
The rule of the area of the sector is
[tex]A=\frac{\emptyset}{360}\times\pi\text{ }\times r^2[/tex]The angle is 77 degrees
The diameter is 6 feet
The radius is half the diameter, then
The radius = 6/2 = 3 feet
Substitute the values of the angle and the radius in the rule above
[tex]A=\frac{77}{360}\times\pi\times(3)^2=6.0475658=6.0\text{ square f}eet[/tex]So the answer is D
The area of the damaged section is 6.0 square feet
A rectangular prism is shown. 8 ft 11 ft 2 ft Which expression can be used to find the lateral surface area of the prism?A (8+2) • 11 B (8 + 2 + 11) • 11C (8+2 +8+2) • 11D (8+2+8+2) 11 +2(8•2)
Let's begin by identifying key information given to us:
The shape is a rectangular prism
The lateral surface area of the prism is given by the formula:
[tex]undefined[/tex]A house is $299,000. You make a 20% down payment and interest payment is $692.68. How much of the first payment for the 30 year loan is interest?
Let's begin by listing out the information given to us:
Cost of house (C) = $299,000
Down payment (D) = 20% = 20% of $299,000
[tex]\begin{gathered} D=\frac{30}{100}\cdot299000=89700 \\ D=89700 \end{gathered}[/tex]D = $89,700
Interest payment (I) = $692.68
30 year loan = (30 * 12) = 360 payments
If the slope of one line is 7/8, what is the slope of the line that is perpendicular to it?88/71/7-1/8-8/7
Given:
Slope of the line 7/8
Slope of the perpendicular line is:
The multiplication of both line should be equal to -1
that mean:
[tex]m_1m_2=-1[/tex]Where m1 and m2 slopes of perpendicular line:
that mean:
[tex]m_1=\frac{7}{8}[/tex]Then slope of perpendicular line is:
[tex]\begin{gathered} m_1m_2=-1 \\ m_2=-\frac{1}{m_1} \\ m_2=-\frac{1}{\frac{7}{8}} \\ m_2=-\frac{8}{7} \end{gathered}[/tex]So slope of perpendicular line is -8/7
If Jake makes 5 out of every 7 shots he makes at the free throw line. What is the ratio of shots made to total shots?a7 to 5b5 to 2C5 to 7d7 to 2
Given:
5 shots made every 7 total shots
Shots made = 5
Total shots = 7
In this question, we are asked to find the ratio of shots made to total shots.
Given that there are a 5 shots made
Jim Goodman, an employee at Walgreens earned 35,000 an increase of 17.6% over the previous year. What were Jim’s earnings the previous year? ( round to the nearest cent)
Last year earnings = X
Present Year earnings = $35,000
Increase = 17.6% = 0.176
[tex]X\cdot(1+0.176)=35000[/tex]This means, that last year earnings multiply by 1.176 equals the present earnings
If we solve for x:
[tex]x=\frac{35000}{1.176}=29761.90[/tex]We found that last year Jim used to earn $29,761.90
The following chart shows the number of months a savings account has been open and the balance of the account. Find the slope of the line through these points. Number of Balance Months (dollars) 1 $400 5 $800 7 $1,000 10 $1,300 D 80 D. 100 UD 100 80
SOLUTION
To find the slope, let us take two y-values and two x-values. This becomes
[tex]\begin{gathered} y-\text{values 800 and 400} \\ x-\text{values 5 and 1} \end{gathered}[/tex]The slope becomes
[tex]\begin{gathered} m=\frac{change\text{ in y}}{\text{change in x}} \\ m=\frac{800-400}{5-1} \\ m=\frac{400}{4} \\ m=100 \end{gathered}[/tex]Hence the answer is 100, the third option.
Fill in the blanks below.Find the slope of the line passing through the points (3,7) and (3,-4).slope: 0Find the slope of the line passing through the points (-2,5) and (9,5).slope: 0
Part a
we have the points (3,7) and (3,-4)
Note that the x-coordinates are equal
that means
Is a vertical line (parallel to the y-axis)
that means
the slope is undefinedVerify
m=(-4-7)/(3-3)
m=-11/0 ----> undefined
Part b
we have the points (-2,5) and (9,5)
Note that the y-coordinates are equal
That means
Is a horizontal line (parallel to the x-axis)
The slope is zeroVerify
m=(5-5)/(9+2)
m=0/11
m=0
A cylinder has a volume of 3204 cubic inches and a height of 5 inches. What is the radius of the cylinder?
The volume of a cylinder can be calculated using the following formula:
[tex]V=\pi r^2h[/tex]To determine the radius of the cylinder, given that we know its volume and hei
The expression -2(u-v)2 evaluated for.u = -3 and v =2
Answer:
-50
Step-by-step explanation:
We are given the following expression:
-2(u - v)²
To evaluate for u = -3 and v = 2, we replace u by -3 and v by 2.
So
-2(-3 - 2)² = -2(-5)² = -2(25) = -50
I’d very much appreciate some help!I was tested on this question and didn’t know how to solve it much, this is new material for me. I need a step by step tutorial with reasons! Thank you!
Answer:
The value of x is;
[tex]x=4[/tex]Explanation:
From the question, it was stated that line BD bisects(divide into two equal halves) angle ABC.
So, angle ABD will be the same as angle CBD.
[tex]\measuredangle ABD=\measuredangle CBD[/tex]Given;
[tex]\begin{gathered} m\measuredangle ABD=7x-10 \\ m\measuredangle CBD=4x+2 \end{gathered}[/tex]substituting the given values we have;
[tex]\begin{gathered} \measuredangle ABD=\measuredangle CBD \\ 7x-10=4x+2 \end{gathered}[/tex]Solving the resulting equation for x, we have;
[tex]\begin{gathered} 7x-10=4x+2 \\ \text{add 10 to both sides;} \\ 7x-10+10=4x+2+10 \\ 7x=4x+12 \\ \text{subtract 4x from both sides} \\ 7x-4x=4x-4x+12 \\ 3x=12 \\ \text{divide both sides by 3} \\ \frac{3x}{3}=\frac{12}{3} \\ x=4 \end{gathered}[/tex]Therefore, the value of x is;
[tex]x=4[/tex]Answer the questions below.(a) Here are the prices in thousands) for 9 houses for sale in a local neighborhood:$163, $285, $286, $ 287, $ 292, $304, $308, $310, $314.Which measure should be used to summarize the data?MeanMedianMode(b) A data set shows the age of each resident at Lakeview Retirement Home.Which measure gives the age shared by the most residents?MeanMedianMode(c) In a survey, 9 people gave the following ratings for a local politician (on a scale of 0 to 100);42, 44, 45, 46, 47, 49, 50, 53, 54.Which measure should be used to summarize the data?MeanMedianModeX
a.
In the first question we need to summarize a set of the prices of houses in a local neighborhood, the best metric to summarize this data is the Median, since the set is assymetrical.
b.
The metric that shows the age shared by most residents is the Mode.
c.
The metric that best represents the ratins is the Mean, as the set is symmetrical and there are not clear outliers.
Solvetheinequality,writeyoursolutioninintervalnotation,andgraphyoursolution.− !! > 10
the inequality is:
[tex]-\frac{2}{5}x>10[/tex]wen can change the sing of the inequality by changing the direction of the inequality sign so
[tex]\frac{2}{5}x<-10[/tex]then we solve for x
[tex]\begin{gathered} x<-10\frac{5}{2} \\ x<-\frac{20}{2} \\ x<-10 \end{gathered}[/tex]The table below gives the distribution of milk chocolate M&M’s. If a candy is drawn at random, what is the probability that it is not orange or red?
To find the probability of the drawn candy to not be red or orange we first need to calculate the probability of it being red or orange. This is done by using the formula below:
[tex]\begin{gathered} P(\text{red or orange) = P(red) + P(orange)} \\ P(\text{red or orange) = 0.13 + 0.2 = 0.33} \end{gathered}[/tex]We now need to find the probability of that not happening. To do that we will subtract that value of 1.
[tex]\begin{gathered} \text{\textasciitilde }P(\text{red or orange) = 1 - P(red or orange)} \\ \text{\textasciitilde }P(\text{red or orange) = 1 - 0.33 = 0.67} \end{gathered}[/tex]The probability of it not being red or orange is 0.67
Trigonometry For the triangle below, find the exact value of cos A
Given
To find the exact value of cos A.
Explanation:
It is given that,
[tex]\begin{gathered} opp.side=8 \\ adj.side=8 \\ hypotnuse=\sqrt{8^2+8^2} \\ =\sqrt{64+64} \\ =\sqrt{128} \\ =8\sqrt{2} \end{gathered}[/tex]That implies,
[tex]\begin{gathered} cosA=\frac{8}{8\sqrt{2}} \\ cosA=\frac{1}{\sqrt{2}} \end{gathered}[/tex]Hence, the exact value of cos A is,
[tex]\frac{1}{\sqrt{2}}[/tex]1Complete the square. Fill in the number that makes the polynomial given below, a perfect-square quadratic.x² - 12x+What would be written in the box
Given the equation:
x² - 12x +
Using completing the square, we are to find the number that will make the above polynomial a perfect-square quadratic.
to get the number that will make the polynomial a perfect square, we consider this form:
x² + bx
To make the polynomial a perfect square quadratic, we divide b by 2 and square it.
That will be:
(b/2)²
b = 12
= (12/2)²
= 6²
= 36
We now have:
x² - 12x + 36 (This makes the polynomial a perfect square quadratic).
the angle of elevation from the top of a 95 foot tall building to a hot air balloon in the sky is 76 degrees . if the horizontal distance between the building in the hot air balloon is 354 ft, what is the height of the hot air balloon from the ground to the nearest tenth?
The situation described is shown in the following picture:
To find the height of the balloon from the ground we first need to find x. From the figure we notice that we have a right triangle and that we want the opposite leg of this triangle. If we remeber the definition of the tangent function:
[tex]\tan \theta=\frac{\text{opp}}{\text{adj}}[/tex]then we have in this case:
[tex]\begin{gathered} \tan 76=\frac{x}{354} \\ x=354\tan 76 \\ x=1419.8 \end{gathered}[/tex]Now we add the value of x to the height of the building:
[tex]95+1419.8=1514.8[/tex]Therefore the height of the balloon is 1514.8 ft
6. 5. Convert each function to slope-intercept form, and then determine in which quadrant the solution falls by graphing the following system of equations. 3x + y = 5 slope-intercept = -9x-3y = 12 slope- intercept = In Ou
The slope intercept form of a line is:
[tex]y=mx+b[/tex]Then we can write each of the equations as:
[tex]\begin{gathered} 3x+y=5 \\ y=5-3x \\ y=-3x+5 \end{gathered}[/tex][tex]\begin{gathered} -9x-3y=12 \\ -3y=12+9x \\ y=\frac{12}{-3}+\frac{9x}{-3} \\ y=-4-3x \\ y=-3x-4 \end{gathered}[/tex]We have parallel lines, as they both have the same slope (m=-3).
If we graph the lines, we get:
The lines don't intersect, so we have no solution.
We can demonstrate this as:
[tex]\begin{gathered} 3x+y=5 \\ -9x-3y=12\longrightarrow3x+y=\frac{12}{-3}=-4 \\ \longrightarrow3x+y=5\ne-4\longrightarrow\text{ no solution (they are not equal)} \end{gathered}[/tex]Use the given right triangle to find ratios, inreduced form, for sin A, cos A, and tan A.
In the given right triangle,
BC=5
AC=12.
Hypotenuse of the triangle, AB=13.
Now, the ratio of sin A can be expressed as,
[tex]\sin A=\frac{opposite\text{ side}}{hypotenuse}[/tex]The opposite side to angle A is BC.
Hence,
[tex]\begin{gathered} \sin A=\frac{BC}{AB} \\ \sin A=\frac{5}{13} \end{gathered}[/tex]The ratio of cos A can be expresssed as,
[tex]\cos \text{ A=}\frac{\text{adjacent side}}{hypotenuse}[/tex]The side adjacent to angle A is AC.
Hence,
[tex]\begin{gathered} \cos \text{ A=}\frac{AC}{AB} \\ \cos \text{ A=}\frac{12}{13} \end{gathered}[/tex]The ratio tan A can be expressed as,
[tex]\begin{gathered} \tan \text{ A=}\frac{\text{opposite side}}{adjacent\text{ side}} \\ \tan \text{ A=}\frac{BC}{AC} \\ \tan \text{ A=}\frac{5}{12} \end{gathered}[/tex]Therefore, sin A=5/13, cos A=12/13 and tan A=5/12.
The Editor-in-Chief of the student newspaper was doing a final review of the articles submitted for the upcoming edition. Of the 12 total articles submitted, 5 were editorials. If he liked all the articles equally, and randomly selected 1 article to go on the front cover, what is the probability that the chosen article is an editorial? Write your answer as a decimal rounded to four decimal places.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
total articles = 12
editorials = 5
P (editorial) = ?
Step 02:
articles selected = 1
P (event) = favorable outcomes / total outcomes
P (editorial) = 5 / 12 = 0.4167
The answer is:
P (editorial) = 0.4167
The range is (- infinity, infinity) and the turning points are (-1.73 , -10.39) and (1.73 , 10.39). What intervals is the function increasing on and decreasing on?
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Show the increasing and decreasing points of the given graphs
STEP 2: Get the intervals of increment and decrement
For intervals where the function is increasing on, we have:
[tex](-1.73,1.73)[/tex]For the intervals where the function is decreasing on, we have two intervals which will be combined using the union sign and will be gotten as:
[tex](-\infty,-1.73)\cup(1.73,\infty)[/tex]