A special commercial about Doritos is to be randomly played during the 210 minutes of the SuperBowl. If you had to leave to run an errand and miss 30 minutes of the game, what is theprobability that you would still be able to see the beginning of the commercial?A. 14.3%B. 12.5%C. 85.7%D. 75%
From the information provided;
A commercial is to be played during the 210 minutes of the super bowl. If you had to miss 30 minutes of the game, the probability of seeing beginning of the commercial would be;
[tex]\begin{gathered} \lbrack P\rbrack=\frac{Total\text{ number of successful events}}{Total\text{ number of }possibl\text{e events}} \\ \lbrack P\rbrack=\frac{30}{210} \\ \lbrack P\rbrack=0.142857\ldots \end{gathered}[/tex]The probability of seeing the beginning of the commercial would be 0.1428 (approximately), and when expressed as a percentage, this would be 14.28%.
ANSWER:
The correct answer therefore is 14.3%
Option A is the correct answer
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Identify the slope and y-intercept of the linear equation then graphY = -2x/7 + 2Y = -5x/6 - 18
For this problem, we are given a certain system of equations and we need to identify the slope, y-intercept and trace the graphs for the system.
The system is given below:
[tex]\begin{cases}y={-\frac{2x}{7}}+2 \\ y=-{\frac{5x}{6}}-18\end{cases}[/tex]Both equations are in the slope-intercept form, which means that the slope is the number multiplying "x" and the intercept is the number isolated.
For equation 1:
[tex]\begin{gathered} \text{ slope}=\frac{-2}{7}\\ \\ \text{ intercept}=2 \\ \end{gathered}[/tex]For equation 2:
[tex]\begin{gathered} \text{ slope}=\frac{-5}{6} \\ \text{ intercept}=-18 \end{gathered}[/tex]The slope is the increase on the graph that the y-axis has for each 1 unit increase in the x-axis. This means that from x = 0 to x = 1 the first equation will decrease 2/7 units and the second equation will decrease 5/6 units. The y-intercept is the point at which the function crosses the y-axis.
With this we can create the graphs:
Solve for y.
5y²+15y=0
the segment joining (-8,1) and (11,7) is divided into four equal parts. Find the points of division nearest to ends.
Midpoint of line is:
[tex]\begin{gathered} (\frac{x_1+x_2}{2}_{},\frac{y_1+y_2}{2}) \\ (\frac{-8+11}{2},\frac{7+1}{2}) \\ (\frac{3}{2},4) \end{gathered}[/tex]Distance between two point.
x distance between F and G :
[tex]\begin{gathered} X=11-(-8) \\ =19 \end{gathered}[/tex]Y distance is:
[tex]\begin{gathered} Y=7-1 \\ =6 \end{gathered}[/tex]For 4 equal part is x and y distance is:
[tex]\begin{gathered} x\text{ distance=}\frac{19}{4}=4.75 \\ y\text{ distance=}\frac{6}{4}=1.5 \end{gathered}[/tex]so x and y coordinates is:
[tex]\begin{gathered} (-8+4.75,1+1.5)_{} \\ (-3.25,2.5) \end{gathered}[/tex]second coordinates is:
[tex]\begin{gathered} (-3.25+4.75,2.5+1.5) \\ (1.5,4) \end{gathered}[/tex]Then theird coordinates is:
[tex]\begin{gathered} (1.5+4.75,4+1.5) \\ (6.25,5.5) \end{gathered}[/tex]Fourth coordinates is:
[tex]\begin{gathered} (6.25+4.75,5.5+1.5) \\ (11,7) \end{gathered}[/tex]
Which row of the input/output table is incorrect?y = 2x - 3xyRow A33Row B57Row C711Row D1015options:Row DRow ARow BRow C
Given:
[tex]y=2x-3[/tex]xy
Row A33
Row B57
Row C711
Row D1015
Required:
To find the row of the input/output table that is incorrect.
Explanation:
The row D is incorrect.
Because, when x=10
[tex]\begin{gathered} y=2(10)-3 \\ =20-3 \\ =17 \end{gathered}[/tex]Final Answer:
Row D is incorrect.
Two more than the quotient of a number and 6 is 4.
The algebraic equation of the English statement is (x/6) + 2 = 4 and the value of the unknown number is 12.
How to determine an algebraic equation from an English statement?Given the statement in the question;
'Two more than the quotient of a number and 6 is 4'
First, we translate into an algebraic equation;
Let the unknown number be represented by x
Two more than ⇒ + 2The quotient of a number and 6 ⇒ x/6is 4 ⇒ = 4Now, we combine;
(x/6) + 2 = 4
This is the algebraic equation of the English statement.
Next, we can solve for the unknown number 'x'
(x/6) + 2 = 4
Subtract 2 from both sides
(x/6) + 2 - 2 = 4 - 2
(x/6) = 4 - 2
(x/6) = 2
Cross multiply
x = 2 × 6
x = 12
Therefore, the numerical value of the unknown number "x" is 12.
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y = 3x -4
m:
b:
Proportional?
(Yes or No) j
-23 < 4x-7 Huryyyyyy
We have the inequality -23 < 4x-7. Our aim is to have X on its own on the left of the inequality sign:
It is important to remember that every operation performed, must be performed on each side of the inequality, in this first step we are adding 7 on the right side and subtracting 7 on the left side.
[tex]\begin{gathered} -23+7<4x-7+7 \\ -16<4x \end{gathered}[/tex]We are going to pass x from the right side to the left side, by doing this we must also change the direction of the inequality:
[tex]4x>-16[/tex]Then we divide by 4 on each side:
[tex]\begin{gathered} \frac{4x}{4}>\frac{-16}{4} \\ x>-4 \end{gathered}[/tex]Craig left his house at noon and drove 50 miles per hour until 3 p.m. Then he drove the next
5 hours at 70 miles per hour.
Graph Craig’s driving trip and calculate the average rate of change for the entire trip
Answer:
62.5 mph
Step-by-step explanation:
rate * time = distance
50 * 3 = 150 mi
70 * 5 = 350 mi
total miles = 500 mi
total time = 8 hrs
Average = 500 mi / 8hr = 62.5 mi / hr
help me please
thank you
Consider the function y = f(x) to have an independent variable x and a dependent variable y. If a function f provides a way to successfully produce a single value y using a value for x, that chosen x-value is said to belong to f's domain.
The Domain of the function is [ -8, 2].
How do you find the domain of a function?Consider the function y = f(x) to have an independent variable x and a dependent variable y. If a function f provides a way to successfully produce a single value y using a value for x, that chosen x-value is said to belong to f's domain.The domain of a function is the set of values that can be plugged into it. This set contains the x values in a function like f. (x). A function's range is the set of values that the function can take. This is the set of values that the function returns after we enter an x value.The Domain of the function is [ -8, 2].
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Identify an inequality you can use to find the possible values of X. Perimeter <51.3 inches
Let's first get the value of x, since it's a right triangle, we use Pythagorean Theorem.
Let's make,
a = 14.2
b = 15.5
c = x
[tex]a^2+b^2=c^2[/tex][tex](14.2)^2+(15.5)^2=x^2[/tex][tex]\text{ x = }\sqrt[]{14.2^2+15.5^2}[/tex][tex]\text{ x = 21.02}[/tex]Let's try choice c if the inequality fits,
[tex]14.2\text{ }+\text{ 15.5 + x }<\text{ }51.3[/tex][tex]14.2\text{ }+\text{ 15.5 + 21.02 }<\text{ 51.3}[/tex][tex]50.72\text{ }<\text{ 51.3}[/tex]The inequality fits, therefore c is the correct answer.
A man realizes he lost the detailed receipt from the store and only has the credit card receipt with the after-tax total. If the after-tax total was $236.72, and the tax rate in the area is 7.6%, what was the pre tax subtotal?
Let's call x to the pre-tax subtotal
Then, the amount of money he pays in taxes is: 0.076x
Therefore, the total cost is: x + 0.076x, which is equal to $236.72. That is:
x + 0.076x = 236.72
1.076x = 236.72
x = 236.72/1.076
x = 220
The pre-tax subtotal was $220
a ramp is built to reach a doorway that is 9 feet off the ground. the ramp makes a 37 angle with the driveway. how long is the ramp
The length of the ramp from the doorway is 11.94ft
What is Trigonometric RatioIn mathematics, the trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry.
To solve this problem, we are going to look at SOHCAHTOA and see which of the ratios fit in this problem.
Adjacent = xOpposite = 9ftAngle = 37 degreeUsing Tangent of an angle, we can find the length of the ramp.
[tex]tan\theta = \frac{opposite}{adjacent}[/tex]
Let's substitute the values into the equation and solve.
[tex]tan 37 = \frac{9}{x} \\x = 11.94ft[/tex]
The length of the ramp is 11.94ft
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Please help I have trouble on these...
The value of a is 5, b is 4, c is 0, d is 3, e is 6 and R is 6 after following the long division method.
According to the question,
We have to divide 430 by 8 by following the long division method.
Note that when we follow long division method then the number by which we are dividing (divisor) is to be multiplied in such a way that the result remains less than the number in the dividend.
Now, we will solve it step by step.
In dividing 43 by 8, we have to multiply 8 by 5. Then, we get 40.
So, we have a = 5, b = 4 and c = 0.
Now, after this we have 30 and the number that we get after multiplication is 24. So, 3 has to be multiplied in 8 to get 24.
So, we have d = 3.
Now, when we will subtract 24 from 30, we will get 6.
So, we have e = 6.
And e is also the remainder, R. So, we have R = 6.
Hence, the values of a, b, c, d, e, and R are 5, 4, 0, 3, 6, and 6 respectively.
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A certain model of TV costs 680 euros. An upgraded model of this TV costs € 782. Calculate a few percent more expensive upgraded model of this TV.
Solution
First find the difference
[tex]782-680=102[/tex][tex]\begin{gathered} \text{ \% increase=}\frac{102}{680}\times100\text{ \%} \\ \\ \operatorname{\%}\imaginaryI\text{ncrease=0.15\times100{\operatorname{\%}}} \\ \\ \operatorname{\%}increase=15\text{ \%} \\ \end{gathered}[/tex]The final answer
The few percent more expensive upgraded model of the TV is
[tex]15\text{ \%}[/tex]In a bag there are green, yellow and orange marbles. The ratio of green to yellow marbles is 2 to 5. The ratio of yellow to orange marbles is 3 to 4. What is the ratio of green to orange marbles?
We have to simplify the ratios to make them comparable;
If the ratio of green to yellow marbles is 2 to 5 and
The ratio of yellow to orange marbles is 3 to 4.
[tex]\begin{gathered} \text{Green to yellow = }2\colon5 \\ \text{Yellow to Orange=3 : 4} \\ \text{Multiply the gr}een\text{ yellow ratio by 3, multiply the yellow-orange ratio by 5, we obtain;} \\ \text{Green to yellow becomes = 6 : 15} \\ \text{Yellow to orange becomes = 15 : 20} \end{gathered}[/tex]Now we can rewrite the ratios of green: yellow : orange as
[tex]6\colon15\colon20[/tex]From this, we can see that the ratio of green to orange marbles is;
[tex]\begin{gathered} 6\colon20 \\ or\text{ in simplest terms} \\ 3\colon10 \end{gathered}[/tex]Therefore, the ratio of green to orange marbles is 3 : 10
Is it a function?, then state the domain and range in set notation,
It is a function.
Because none of the values of the domain is repeated
the domain in set notation
[tex]x=\lbrace1,3,5,7\}[/tex]the range in set notation is
[tex]y=\lbrace-1,4,6\rbrace[/tex]What is (2x)(3x) in words but not explaining how to get the answer?
The number (2x)(3x) in the word will be two time the variable multiplied the three times the variable.
What is termed as the variable?A variable is a property that can be assessed and has multiple values. Variables can be divided into two types: categorical and numeric. The categories are further subdivided into two subgroups: ordinal or nominal for categorical variables and discrete as well as continuous for numeric variables.For the given question,
The number in digits is given as (2x)(3x).
The 'x' is the variable part who value is not defined for the question.
Thus, twice the variable will be 2x.
Thrice the variable will be 3x.
The multiplication of both the numbers will be (2x)(3x).
Therefore, in words the number will be written as two time the variable multiplied the three times the variable.
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Help me please! It’s an emergency!! A small company is selling a new board game, and theyneed to know how many to produce in the future.They sold a total of 400 games after 11 months, 800games after 21 months, and 1500 games after 36months. Is a single linear model a reasonable option for this data? Use this to estimate the number of games sold after 48 months. Explain.
Based on the data given:
400 games were sold after 11 months
800 games were sold after 21 months
1500 games were sold after 36 months
We need to plot a graph of months against the number of games:
From the graph,
Yes, a single linear model is a reasonable option for the data
The equation of the graph is given by:
[tex]y\text{ = 0. 0226x + 2.344 }[/tex]Note that y represents the number of months and x represents the number of board games.
The number of board games sold after 48months simply means that y= 48. In order to get x, we substitute y = 48 into the model
[tex]\begin{gathered} 48\text{ = 0.0226x + 2.344} \\ 0.0226x\text{ = }48-2.344 \\ 0.0226x\text{ =45.656} \\ x=\frac{45.656}{0.0226}=2020.18\text{ (to 2 d.p)} \end{gathered}[/tex]Therefore, the estimated number of games sold after 48 months is 2020.
fourteen percent of the town's population are above age of 65. if there are about 320 residents over the age of 65, then what is the towns population?
Town Total population is 2,286.
To Find total population :To get the population of the town, we can solve this for x.We are given that 14% of a town's population is over the age of 65.320 residents of the town are over the age of 65.Therefore, 14% of the town's population is equal to 320.
so we will let the towns population be x.
We can convert this to our percent equation to get the following:14/100 * x = 320
To get the population of the town, we can solve this for x. We'll start by multiplying 100 both sides of the problem14x =32,000
Now, we divide both sides of the equation by 14.x =2285.
So we have that the town's population is approximately 2,286 people.
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Given that f(x)= x^2-1x and g(x)= x+8 calculate f•g(x)
K
What is the weight of a 35.01-carat diamond in grams and ounces? Use 1 carat = 0.2 gram, 1 carat-3.086 grains, and 1 ounce = 437.5 grains.
The weight of a 35.01-carat diamond is 9.
(Round to two decimal places as needed.)
The weight of a 35.01-carat diamond is oz.
(Round to two decimal places as needed.)
twenty soldiers were walking in a forest, they saw an apple tree with 20 apples on it, each took one. how many apples remained?
In 2006, the population of Tewksbury, Rhode Island was 25,000, and it was growing at an annual rate of 2.2%.Part AWhat is the growth factor for the town?Part BWrite an equation to model the cars value.Part CUse your equation to estimate the population of Tewksbury in 2011. round your response to the nearest whole number
Part A. To find the growth factor of the town, you can proceed like this
[tex]\begin{gathered} 2.2\text{ \% }=\frac{2.2}{100}=0.022 \\ \text{Then,} \\ 25000\cdot0.022=550\Rightarrow\text{ Population increase in one year} \\ 25000+550=25550\Rightarrow\text{ Population in 2007},\text{ adding the population in 2006 plus the increase} \\ \end{gathered}[/tex]So, the growth factor for the town will be
[tex]\frac{25550}{25000}=1.022[/tex]For part B, exponential growth is modeled by the equation
[tex]\begin{gathered} y=ab^x \\ \text{Where} \\ a\text{ is the initial amount} \\ b\text{ is the growth factor} \\ x\text{ is the time in years} \end{gathered}[/tex]So, you have
[tex]\begin{gathered} a=25000 \\ b=1.022 \\ \text{ Then,} \\ y=(25000)(1.022)^x \end{gathered}[/tex]For part C, you need to find the population in 2011, so
[tex]2011-2006=5\text{ years}[/tex]Then, plug in the equation found x = 5
[tex]\begin{gathered} y=(25000)(1.022)^x \\ y=(25000)(1.022)^5 \\ y=27873.7 \\ \text{Rounding} \\ y=27874 \end{gathered}[/tex]Therefore, the population of Tewksbury in 2011 will be 27874 people.
Write a linear equation for thw line that goes through the point (2,5) and has a slope of 2.
Given:
Point; (x, y) ==> (2, 5)
Slope, m = 2
To write a linear equation that goes through the point, apply the slop-intercept form:
y = mx + b
Where m is the slope and b is the y-intercept.
Take the following steps:
• Step 1:
Substitute 2 for m.
Input the points (2, 5) for the values of x and y repsectively
y = mx + b
5 = 2(2) + b
5 = 4 + b
• Step 2:
Solve for b.
Subtract 4 from both sides
5 - 4 = 4 - 4 + b
1 = b
Therefore, to write the linear equation, substitute 2 for m, and 1 for b in (y = mx + b)
y = mx + b
y = 2x + 1
Therefore, the equation for the line that goes through the point (2, 5) and has a slope of 2 is:
y = 2x + 1
ANSWER:
[tex]y=2x+1[/tex]
In a certain year, the annual per capita consumption of eggs was 496; that is the average person ate 496 eggs per year. Ina year many decades later, the annual per capita consumption had dropped to 255. Round each annual per capita consumption to the nearest ten. A) earlier year had (blank) eggs B) more recent year had (blank) eggs C) in more recent year, the average person ate (blank) as many eggs as the average person did in the earlier year.
Ok, so
We know that the annual per capita consumption of eggs was 496, and it dropped to 255.
So, We need to find the fraction eggs the average person eats in the first year as the average person did in the last year. We are given, per capital consumption of eggs in the first year = 496 and, per capital consumption of eggs in the last year = 255.
Then, earlier year had 496 eggs.
More recent year had 255 eggs.
We can say that in more recent year, the average person ate 0.5 as many eggs as the average person did in the earlier year.
0.5 comes from divide 255/496, that means that the average person ate 0.5 times eggs than the people who ate in the earlier year.
The sum of two numbers is -32. One number is two less than the other.
ANSWER:
EXPLANATION:
Let x and y be the two numbers
Find the HCF and lcm of 42 72 and 90 and multiply it together
Answer:
Step-by-step explanation:
HCF of 42,72 and 90
=6
LCM of 42,72 and 90
=2520
2520 x 6 = 15120
=15120
Simplify:(4 7- 5m) + 32m - 16
Kmakq, this is the solution:
Let's simplify:
4 (7 - 5m) + 32m - 16
28 - 20m + 32m - 16
12m + 12
12 (m + 1) is the final answer
Answer:
Step-by-step explanation:
Use the given functions to set up and simplify
7
−
5
m
+
32
m
−
16
.
4
=
7
−
5
m
+
32
m
−
16
=
27
m
−
9
