In probability, A is 8 out of 16 and C is 3 out of 15.
What is probability explain?
The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities.Out of the 17 counters in the bag 3 are yellow , 6 are red and the rest i.e., 17–3–6 or 8 nos.are green.
When selected randomly once one counter the probability of selecting one is
A. green is 8 out of 17 or 8/17 ,
B. getting a red one is 6 out of 17 or 6/17.
C. getting a yellow is 3 out of 17.
This is when the counter is put back in the bag for selecting.
If the selected one is not put back remaing counters are less by one each time it's drawn and then the probability figure is one out of 16 in the second case and one out of 15 for the third draw ime., then A is 8 out of 16 and C is 3 out of 15.
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Find the complement of the set given that U= {3,4,5,6,7,8,9,10,11} (use the roster method to write the set. Enter empty or 0 the empty set.) {5,7,9,10}
Let
[tex]\begin{gathered} U=\mleft\lbrace3,4,5,6,7,8,9,10,11\mright\rbrace \\ \text{and} \\ A=\mleft\lbrace5,7,9,10\mright\rbrace \end{gathered}[/tex]Then,
[tex]\begin{gathered} A^C=U-A=\lbrace3,4,5,6,7,8,9,10,11\rbrace-\lbrace5,7,9,10\rbrace=\mleft\lbrace3,4,6,8,11\mright\rbrace \\ \Rightarrow A^C=\lbrace3,4,6,8,11\rbrace \end{gathered}[/tex]Thus, the answer is {3,4,6,8,11}
hey please help. this has to do with exponential functions. i have to do 225 problems before midnight. it’ll mean a lot!!!
Answer:
Explanation:
To complete the missing values, we have to evaluate the function at the x-values given.
For example, to find the number below x = -1, we will put in x = -1 into y = (1/6)^x.
Putting in x = - 1 in y = (1/6)^x gives
[tex]y=(\frac{1}{6})^{-1}[/tex]which simplifies to give
[tex]y=\frac{1}{1/6}[/tex][tex]\rightarrow y=6[/tex]Similarly, for the missing value below x = -2, we put in x = - 2 into y = (1/6)^x to get
[tex]y=(\frac{1}{6})^{-2}[/tex]which simplifies to give
[tex]y=\frac{1}{(1/6)^2}[/tex][tex]\begin{gathered} \rightarrow y=6^2 \\ \rightarrow y=36 \end{gathered}[/tex]Similarly, for the missing value below x = 2, we put in x = 2 in y = (1/6)^x to get
[tex]y=(\frac{1}{6})^2[/tex]which simplifies to give
[tex]y=\frac{1}{36}[/tex]Hence, the missing value to be put in is 36.
To summerise, the missing values are
x | -2
part 2..number 2...evaluate the expressions using numbers and evaluate the expression for the numbers provided...please read the direction to make sure I'm understanding what's asked of me..I'm a 7th grader can u please help me with my math summer package and explain it in a way that a 7th grader can understand it
Given:
Each story is 13ft tall.
Explanation:
a) To find: The height of the skyscraper if it has 55 stories.
Since the number of stories increases the height of the skyscraper also increases.
That is,
[tex]\begin{gathered} h=Number\text{ of stories}\times Height\text{ of each story} \\ h=55\times13 \\ =715ft \end{gathered}[/tex]b) To find: The height of the skyscraper if it has 65 stories.
The height of the skyscraper would be,
[tex]\begin{gathered} h=Number\text{ of stories}\times Height\text{ of each story} \\ h=65\times13 \\ =845ft \end{gathered}[/tex]c) To find: The height of the skyscraper if it has 75 stories.
The height of the skyscraper would be,
[tex]\begin{gathered} h=Number\text{ of stories}\times Height\text{ of each story} \\ h=75\times13 \\ =975ft \end{gathered}[/tex]d) To find: The equation of the height if it has f stories
The height of the skyscraper would be,
[tex]\begin{gathered} h=Number\text{ of stories}\times Height\text{ of each story} \\ h=f\times13 \\ h=13f \end{gathered}[/tex]Final answer:
a) The height of the skyscraper if it has 55 stories is 715ft.
b) The height of the skyscraper if it has 65 stories is 845ft.
c) The height of the skyscraper if it has 75 stories is 975ft.
d) The expression that represents the height of f stories is h = 13f.
M is the midpoint of line AB. Endpoint A is (4, 2). Midpoint M is (6, 0). Endpoint B = ?
The B points are ( 8, -2 ) of Endpoint B when M is the midpoint of line AB.
What is midpoint of a segment?
The midway of a line segment in geometry is where it meets the other end. The centroid of the segment and the endpoints, it is equally spaced from both endpoints. It cuts the section in half.M is the midpoint of line AB.
Endpoint A is (4, 2).
Midpoint M is (6, 0)
Let mid points are ( x,y) and A points are ( x₂ , y₂ ) and B points are ( x₁ , y₁)
x = x₁ + x₂/2 , y = y₁ + y₂/2
6 = x₁ + 4/2 , 0 = y₁ + 2/2
12 = x₁ + 4 , 0 = y₁ + 2
x₁ = 12 - 4 , y₁ = -2
x₁ = 8 , y₁ = -2
So, the B points are ( 8, -2 )
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Shaun estimated that the attendance at a college baseball game was 1,000. The actual Q3: attendance was 1,788. What is the percent error of Shaun's estimate? Round to the nearest whole percent.
The percentage error of Shaun's estimate is 44%
Here, we want to get the percentage error
We can get this by using the formula below;
[tex]\frac{error}{\text{actual value}}\text{ }\times\text{ 100\%}[/tex]We have the error as the difference between the estimated value and the actual value
The difference is;
[tex]1,788\text{ - 1,000 = 788}[/tex]The percentage error is;
[tex]\frac{788}{1,788}\text{ }\times\text{ 100 \% = 44.07 }[/tex]This is approximately 44%
Calculate the correlation coefficient for the given data below:
x y
2 21
3 22
48
5 11
6 15
7 14
Round your final result to two decimal places.
The correlation coefficient of the data provided is -0.52.
What is the correlation coefficient?Correlation is a measure that is used in statistics to determine the linear relationship that exists between two variables. Correlation can be positive, negative or zero.
Positive correlation is when two variables move in the same direction. Negative correlation is when two variables move in opposite directions. Zero correlation is when there is no relationship between the variables.
Correlation can be determined using a financial calculator. When the financial calculator is used, the correlation coefficient is -0.52
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What type of reasoning is used to find the next amount of train cars? Explain your answer.
The type of reasoning used to find the next amount of train cars is an arithmetic sequence, it can be assumed that the next amount of train cars that in the sequence is 6.
What is an arithmetic sequence?The difference between successive words in an arithmetic series is known as the common difference y. The existence of the nth term of an arithmetic sequence is given by the following rule:
x1 = x1 + (n-1)y;
Where x1 is the first term.
In the context of this problem, from the image, the number of train cars can be modeled by the following sequence exists (0, 2, 4, ...).
Which exists an arithmetic sequence with:
The first term of 0.A common ratio of 2.Therefore the next term of the sequence is given by:
4 + 2 = 6.
This is because 4 is the last term and 2 is the common ratio.
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M&Ms Data Set 20 in Appendix B lists data from 100 M&Ms, and 8% of them are
brown. Use a 0.05 significance level to test the claim of the Mars candy company that the
percentage of brown M&Ms is equal to 13%.
The rejection region, or area of the rejection zone, is the significance level. The test's tail determines the direction of the rejection region. When the significance threshold is unknown, it is typically considered to be 5%.
What is rejection region ?A collection of values for the test statistic for which the null hypothesis is rejected constitutes a critical zone, sometimes referred to as the rejection region. For example, if the observed test statistic is in the critical range, the null hypothesis is rejected and the alternative hypothesis is accepted.
Consider the crucial value as a cut-off point at a particular importance level. If a test statistic falls on one side of the crucial value and leads to the null hypothesis being accepted, a test statistic falling on the other side will lead to the null hypothesis being rejected.
A set of values for the test statistic for which the null hypothesis is accepted is referred to as a confidence interval and is also referred to as the acceptance area. For example, if the observed test statistic is within the confidence interval, the null hypothesis is accepted and the alternative hypothesis is rejected.
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A runner sprinted 365.21 ft to finish a race.Use the table of facts to find the distance she sprinted in yards.Round your answer to the nearest tenth.
we have the following:
[tex]365.21ft\cdot\frac{1y}{3ft}=121.74[/tex]Therefore, the answer is 121.7 yards
what is the equation for the line passing through the points: (3,-10.5) and (1,-7.5)
The equation of the line passing through the points: (3,-10.5) and (1,-7.5) is [tex]3x+2y+12=0.[/tex]
How to find equation of a line by two-point form?Every point on a line fulfills the equation of that line, which means that every point on the line represents every other point on the line.
The equation of a line passing through two-points [tex](x_{1} ,y_{1} )[/tex] and [tex](y_{1} ,y_{2} )[/tex] is given by the formula,
[tex]y-y_1= \frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
So, the equation of the line passing through the points (3,-10.5) and (1,-7.5) will be-
⇒[tex]y-(-10.5)=\frac{-7.5-(-10.5)}{1-3} *(x-3)[/tex]
⇒[tex]y+10.5=\frac{-7.5+10.5}{-2} *(x-3)[/tex]
⇒[tex]y+10.5=\frac{3}{-2} *(x-3)[/tex]
⇒[tex]y+10.5=\frac{-3x}{2} +\frac{9}{2}[/tex]
⇒[tex](y+10.5)*2=-3x+9[/tex]
⇒[tex]2y+21=-3x+9[/tex]
⇒[tex]2y+3x+21-9=0[/tex]
⇒[tex]3x+2y+12=0[/tex]
Hence, the equation of the line passing through the points (3,-10.5) and (1,-7.5) is [tex]3x+2y+12 =0[/tex].
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Two buses leave Philadelphia at the same time and travel in opposite directions. The north bound bus travels
at a rate of 55 mph. The southbound bus travels at a rate of 45 mph. When will they be 400 miles apart?
Answer:
4 hours
Step-by-step explanation:
55x + 45x = 400
100x = 400
x = 400/100
x = 4
One interior angle of a triangle is 98.5°, and the other two interior angles are congruent. What is the degree measure of one of the congruent angles?
81.5°
90°
40.75°
49.25°
Answer:
(c) 40.75°
Step-by-step explanation:
Given an isosceles triangle with one angle 98.5°, you want the measures of each of the other two angles.
Angle sum theoremThe sum of angles in a triangle is 180°, so we have ...
2x + 98.5° = 180° . . . . . . x is the unknown angle measure
x +49.25° = 90° . . . . . . divide by 2
x = 40.75° . . . . . . . . . . subtract 49.25°
The measure of one of the congruent angles is 40.75°.
What is the value of y?
2
4
6
8
Answer: Ima say 6
Explanation: I don't have an explanation
b) Describe the function over each part of its domain. State whether it is constant,
increasing, or decreasing, and state the slope over each part.
Description of the function over each part of its domain is:
Slope = 0 and the domain is constant at (0,12000).Domain (12000, 38000) is declining with a negative slope.What is a function?A function is a type of rule that produces one output for a single input. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would say that y is a function of x.So, we examine the displayed graph.
The y values are constant from x = 0 to x = 12,000.
There is no increase or decrease in y's value; it is constant.Consequently, the graph's cost is constant from x=0 to x=12000.So slope = 0.
Then,
Slope = 0 and the domain is constant at (0,12000).
The y values are decreasing from x = 12,000 to x = 38,000.The slope is negative for y values that are decreasing.The slope is therefore negative.Domain (12000, 38000) is declining with a negative slope.
Therefore, description of the function over each part of its domain is:
Slope = 0 and the domain is constant at (0,12000).Domain (12000, 38000) is declining with a negative slope.Know more about functions here:
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what is the effect on the graph of the function f(x) = x² when f(x) is changed to f(x) + 9A) shifted up B) shifted left C) shifted rightD) shifted down
When we add a constant on a f(x) graph we have
• f(x) + a ⇒ graph shifted up
,• f(x) - a ⇒ graph shifted down
Therefore, let's see if it's shifting up or down, we have
[tex]f(x)+9[/tex]9 is positive, then it's shifting up 9 units.
please help me identify what was wrong in solving it I know the right answer is 10 but i don't know what was done wrong.
Given:
The coordinates are given as,
[tex]\begin{gathered} (x_1,y_1)=(-1,2) \\ (x_2,y_2)=(-7,-6) \end{gathered}[/tex]The objective is to find the distance between the two points.
Explanation:
The general formula to find the distance between two coordinates is,
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}\text{ . . . . . (1)}[/tex]Substitute the given coordinates in equation (1),
[tex]d=\sqrt[]{(-7-(-1))^2+(-6-2)^2}[/tex]On further solving the above equation,
[tex]\begin{gathered} d=\sqrt[]{(-6)^2+(-8)^2} \\ =\sqrt[]{36+64} \\ =\sqrt[]{100} \\ =10 \end{gathered}[/tex]Hence, the distance between the two points is 10.
Find the value of x and y in which each quadrilateral mist be a parallelogram.
Recall the property of parallelograms that tell us that the diagonals intercept producing equal segments in each of them. Then, as the diagonals intercept in the midpoint of each diagonal, then we can create the following equations and solve them one at a time (making the measure of one segment equal the value on the other half of the diagonal):
5 y - 4 = 36 then we solve here for y
add 4 to both sides
5 y = 36 + 4
5 y = 40
divide both sides by 5
y = 40 / 5
y = 8
Now the second equation:
4 x - 10 = 18
add 10 on both sides
4 x = 28
divide both sides by 4 to isolate x
x = 28 / 4
x = 7
In this diagram, ABAC – AEDF. If thearea of ABAC = 6 in2, what is thearea of AEDF?DE2 inFB3 inСArea = [?] in?Enter a decimal rounded to the tenths.
Answer:
8/3 square inches
Explanation:
First, we need to get the height of the triangle BAC
Area of triangle = 1/2 * base * height
6 = 1/2 * 3 * height
12 = 3 * height
Height = 12/3
The height of triangle BAC is 4inches
Next is to get the height of EDF. Since they are both similar hence;
2/3 = h/4
3h = 2 * 4
3h = 8
h = 8/3
h = 8/3in
Hence the height of triangle EDF is 8/3in
Get the area of triangle EDF
Area of triangle EDF = 1/2 * 2 * 8/3
Area of triangle EDF = 8/3 square inches
Hence the area of triangle EDF is 8/3square inches
Find the constant of proportions k as a fraction in simplest form. The enter an equation for the relation ships between x and y.The constant of proportions, k is equal to?The equation is y = ?
Notice that for every 6 units increment in the x-values in the table, there is a 2 units increment in the y-values.
Therefore, the constant of proportions is:
[tex]\begin{gathered} \frac{2}{6}\rightarrow\frac{1}{3} \\ k=\frac{1}{3} \end{gathered}[/tex]To find the equation, we'll use this constant as the slope. Using this, point
(6, 2) of the table and the slope-point form:
[tex]\begin{gathered} y-2=\frac{1}{3}(x-6) \\ \rightarrow y-2=\frac{1}{3}x-2 \\ \rightarrow y=\frac{1}{3}x \end{gathered}[/tex]This way the equation is:
[tex]y=\frac{1}{3}x[/tex]I need help with this question please. I have options available
Option B is the graph of the given function.
The students in Hugh Logan's math class took the Scholastic Aptitude Test. Their math scores areshown below. Find the mean score. Round your answer to the nearest tenth.563 524 357 347 637358 351 528 470 482pls be fast
Answer:
[tex]461.7\Rightarrow\text{ Option \lparen D\rparen}[/tex]Explanation: We have to find the mean of the total scores shown, the formula for the mean is as follows:
[tex]A=\frac{a_1+a_2+a_3+a_4+...+a_N}{N}\rightarrow(1)[/tex]Using the formula (1) the mean of the score is calculated as follows:
[tex]\begin{gathered} A=\frac{563+524+357+347+637+358+351+528+470+482}{10} \\ \\ A=\frac{4617}{10}=441.7 \\ \\ A=461.7\rightarrow\text{ \lparen D\rparen} \end{gathered}[/tex]Therefore the answer is Option(D).
Is the coordinate (5,-3) a solution to the following system of equations?
y=2x-13
2x+6y=-8
Yes, the coordinate is a solution to both equations
No, the coordinate is not a solution for either equaiton
No, the coordinate is only a solution for y-2x-13
ordinate is only a solution for 2x+6y=-8
Option (a) is correct.
What is a equation?statement of equality between two expressions consisting of variables and/or numbers. In essence, equations are questions, and the development of mathematics has been driven by attempts to find answers to those questions in a systematic way.
Given that,
The given equation are
y=2x-13 ........(1)
2x+6y=-8 ........(2)
Solve the equation by elimination method
From equation (1)
y-2x = -13
From equation (2)
Now,
y-2x = -13
6y+2x = -8
adding both equation
7y = -21
y = -3
substitute the value of y in equation (1)
y = 2x-13
-3 = 2x-13
-3+13 = 2x
2x = 10
x = 5
Hence, The coordinate (5,-3) is a solution to both equations.
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The number of Americans over age 100 can be approximated by P(t) = 0.07e^0.54t, where is P(t) measured in millions and t is measured in decades. Also, t=0 corresponds to 2000.
a. How many Americans over age 100 were there in 2000?
b. How fast was the number of Americans over age 100 changing in 2000? Use the correct units.
There are 7 % of Americans over age 100 who were there in 2000 and the number of Americans growing by 54% over age 100 changed in 2000.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
It is a relation of the form y = aˣ in mathematics, where x is the independent variable
The number of Americans over age 100 can be approximated by
[tex]P(t) = 0.07e^{0.54t}[/tex]
where is P(t) measured in millions and t is measured in decades.
Also, t = 0 corresponds to 2000.
⇒ [tex]P(t) = 0.07e^{0.54t}[/tex]
Substitute the t = 0 in the above function, and we get
⇒ [tex]P(t) = 0.07e^{0.54\times0}[/tex]
⇒ P(t) = 0.07 e°
⇒ P(t) = 0.07
Convert decimals into fractions, and we get
⇒ P(t) = 7 / 100
This represents 7 out of 100 which is 7 % of Americans over age 100 who were there in 2000.
Thus, the number of Americans growing by 54% over age 100 changed in 2000.
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The diameter of the earth at its equator is about 8000 miles. The diameter of Saturn at its equator is about 74,000 miles. Saturn's diameter is about how many times as large as the Earth's diameter?
A. 9.25×10^3
B. 9.25 × 10^2
C. 9.25×10^1
D. 9.25 x10^0
Answer:
C
Step-by-step explanation:
[tex]\frac{74000}{8000}=9.25 \times 10^1[/tex]
8. For every 1,000 feet above sea level, the air temperature decreases by 4°F.The highest natural point in Texas is Guadalupe Peak at 8,751 feet. If thetemperature at sea level is 76°F, what is the temperature near the summit at8,000 feet? (Example 4)
Answer
The temperature at an altitude of 8,000 feet is 44° F
SOLUTION
Problem Statement
The question tells us that air temperature drops by 4 degrees Fahrenheit for every 1,000 feet above sea level. We are asked to calculate the temperature at 8,000 feet, close to the summit of Guadalupe Peak.
Solution
To solve this question, we simply compute the temperature changes for each 1,000 increase in height and then generalize. With the generalization, we can find the temperature at any height.
The temperature at 0 feet is 76°F (At sea level)
The temperature at 1,000 feet is 76°F - 4°F = 72° F
The temperature at 2,000 feet (2 x 1,000 feet) is 76°F - 4°F - 4°F (76°F - 2 x 4°F)
The temperature at 3,000 feet (3 x 1,000 feet) is 76°F - 4° F - 4° F - 4° F (76° F - 3 x 4° F)
And so on.
We can see a pattern developing and with this pattern, we can make a generalization about the temperature decrease for every increase in altitude.
[tex]\begin{gathered} The\text{ temperature at }n\times1,000\text{ feet is (}76^o-n\times4^o)F \\ \text{where,} \\ n=A\text{ whole number starting from zero} \end{gathered}[/tex]Thus, we can solve the question by substituting n = 8 for an altitude of 8,000 feet. This is done below:
8 x 1000 feet = 8,000 feet is:
[tex]\begin{gathered} 76^oF-8\times4^{o\text{ }}F \\ 76^oF-32^oF \\ =44^oF \end{gathered}[/tex]Final Answer
The temperature at an altitude of 8,000 feet is 44° F
Write this in a equation. 1. three increased by 6 times a number2. ten more than twice a number3. the difference between 4 times a number and 14. 12 less than 3 times a number is negative 65. three times the difference of a number and 126. 2 more than 5 times a number is 17
Answer:
3. the difference between 4 times a number and 1
[tex]4x-1[/tex]5. three times the difference of a number and 12
[tex]3(x-12)[/tex]Explanation:
Writing the equation of the given expressions;
Let x represent the missing number;
3. the difference between 4 times a number and 1
[tex]4x-1[/tex]5. three times the difference of a number and 12
[tex]3(x-12)[/tex]14. If the surface area of the cone below is 628.32 m2, find its volume.
You have a cone with surface area of 628.32 m². In order to find the volume of the cone you use the following formula:
V= 1/3 π r² h
r: radius of the base of the cone = 15m/2 = 7.5m
h: heigth of the cone
Then, you have to calculate first the height of the cone. To do that, you use the information about the surface area. You use the following formula:
S = πr² + πrl
l: diagonal of the cone
Then, you have to find l, and then you can calculate hYou solve for l from the surface area formula:
l = (S - πr²)/πr = (628.32 - π(7.5)²)/(π(7.5))
l = 19.16
To calculate the heigth of the cone you use the Pythagoras theorem, just as follow:
h = √(l²-r²) = √((19.16)²-(7.5)²) = 17.63m
Next, you can replace the values of h and r into the formula for the Volume:
V= 1/3 π r² h = (1/3)π (7.5m)²(17.63m) = 1038.5m³
Hence, the volume of the given cone is 1038.49 m3
A linear function r models the growth of your right index fingernail. The length of the fingernail increases 0.7 millimeter every week. Graph r when r(0)=12.
A nail's length in x weeks of m=0.7 slope with a growth rate of mm per week b starting length follows.
The slope-intercept form of a straight-line equation is indicated by y = mx + b. X and y denote the line's distance from the x- and y-axes, respectively. When x = 0, the value of b equals y, and m indicates how steep the line is.
Given, r(0) = 12
According to the question, fingernail increases by 0.7 millimeters every week. So, m = 0.7 which is the slope of the equation of a straight line.
r(0) = 12 is the b of the y = mx + b.
Now, the final equation is:
r(x) = 0.7x + 12
As a result, the slope of r(x) length of a nail in x number of weeks of m=0.7, with growth rate in mm per week b starting length.
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Technology required. Ramps in a parking garage need to beboth steep and safe. The maximum safe incline for a ramp is8.5 degrees. Is this ramp safe? If not, provide dimensions thatwould make the ramp safe.
Ok, so:
Let me draw the situation here below:
Ok, let's find the angle first:
For this, we shall make use of the trigonometric functions:
In this case, the most useful function which could help us to solve this problem is tan(x). This function relations the opposite side of the angle and its adjacent side, like this:
tan(x) = opposite side / adjacent side
So, if we replace the values:
tan(x) = 15/95
tan(x) = 0,15789474
To find x, we could use the inverse function of tan(x). This one is called arctan(x).
So, arctan(tan(x)) = arctan(0,15789474)
And this is:
x = 8.97 degrees
Now, we can affirm that the angle is 8.97 degrees, which is bigger than 8.5 degrees.
Now, what should be the length of the bottom for the ramp to be safe?
Let me draw the situation:
We know that the ramp is safe if the maximum safe incline is 8.5°. So, what should be the value of x for this occurs?
We use the trigonometric function tan(x) again.
tan(8.5°) = 15/x
Remember that tan(8.5°) is a number
Then, x = 15/tan(8.5°), and this is 100.36
So, we conclude that the lenght of the bottom should be at least, 100.36
Hallie has 10 times as many pages to read for her
homework assignment as Janet. Altogether, they have
to read 264 pages. How many pages
does each girl
have to read?
Answer:
24
Step-by-step explanation:
10x + x = 264
11x = 264
x = 264 ÷ 11
x = 24
therefore hallie has 240 pages and Janet 24
total 264