The probability of landing in any colour is:
[tex]\frac{1}{5}[/tex]so if we want to get a red, both times, we to multiply 1/5 twice
[tex]\frac{1}{5}\cdot\frac{1}{5}=\frac{1}{25}[/tex]so, the probability of getting red twice is 1/25
A rectangular board is 1200 millimeters long and 900 millimeters wide what is the area of the board in square meters? do not round your answer
Answer: Area of the rectangular board is 1.08 square meters
The length of the rectangular board = 1200 milimeters
The width of the rectangular board = 900 milimeters
Area of a rectangle = Length x width
Firstly, we need to convert the milimeter to meters
1000mm = 1m
1200mm = xm
Cross multiply
x * 1000 = 1200 x 1
1000x = 1200
Divide both sides by 1000
x = 1200/100
x = 1.2 meters
For the width
1000mm = 1m
900mm = xm
cross multiply
1000 * x = 900 * 1
1000x = 900
Divide both sides by 1000
x = 900/1000
x = 0.9m
Length = 1.2 meters
Width = 0.9 meter
Area = length x width
Area = 1.2 x 0.9
Area = 1.08 square meters
2 dot plots. Both number lines go from 0 to 10. Plot 1 is titled fifth grade. There are 2 dots above 1, 3 above 2, 1 above 3, 4 above 4, 5 above 5, 5 above 6, 2 above 7, 2 above 8, 0 above 9, 0 above 10. Plot 2 is titled seventh grade. There are 2 dots above 0, 2 above 1, 3 above 2, 5 above 3, 5 above 4, 3 above 5, 3 above 6, 1 above 7, and 0 above 8, 9, and 10.
The dot plot shows the number of hours, to the nearest hour, that a sample of 5th graders and 7th graders spend watching television each week. What are the mean and median?
The 5th-grade mean is
.
The 7th-grade mean is
.
The 5th-grade median is
.
The 7th-grade median is
.
The mean of the 5th grade students is 4.67
The mean of the 7th grade students is 3.46
The median of the 5th grade students is 5
The median of the 7th grade students is 3.5
What are the mean and median?A dot plot is a graph used to represent a dataset. A dot plot is made up of a number line and dots. The dots in the dot plot represent the frequency of the data. The greater the frequency of a data, the greater the number of dots.
Mean is the average of a dataset. It is determined by adding all the numbers in the dataset together and dividing it by the total numbers in the dataset.
Mean = sum of numbers / total numbers in the dataset
Mean of the 5th grade students = ( 1 + 1 + 2 + 2 + 2 + 3 + 4 + 4 + 4 + 4 + 5 + 5 + 5 + 5 + 5 + 6 + 6 + 6 + 6 + 6 + 7 + 7 + 8 + 8 ) / 24
112 / 24 = 4.67
Mean of the 7th grade students = ( 0, 0, 1 + 1 + 2 + 2 + 2 + 3 + 3 + 3 + 3 + 3 + 4 + 4 + 4 + 4 + 4 + 5 + 5 + 5 + 6 + 6 + 6 + 7) / 24
83 / 24 = 3.46
Median is the number that is in the middle of a dataset.
Median = (n + 1) / 2
Median of the 5th grade students = (24 + 1) / 2 = 12.5 terms = 5
Median of the 7th grade students = (24 + 1) / 2 = 12.5 term = (3 + 4) / 2 = 3.5.
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find the measures of the angles of a right triangle where one of the acute angles is *3.5* times the other
Lets draw a picture of our problem:
where x denotes the measure of the base angle.
Since interior angles of any triangle add up to 180, we have
[tex]x+3.5x+90=180[/tex]which gives
[tex]4.5x+90=180[/tex]By subtracting 90 to both sides, we have
[tex]\begin{gathered} 4.5x=180-90 \\ 4.5x=90 \end{gathered}[/tex]Finally, by dividing both sides by 4.5, we get
[tex]\begin{gathered} x=\frac{90}{4.5} \\ x=20 \end{gathered}[/tex]Then, the base angle measures 20 degrees and the upper angle measure
[tex]3.5\times20=70[/tex]Therefore, the searched angles measure
[tex]20,70\text{ and 90}[/tex]What is the product of 3√6 and 5√12 in simplest radical form?
In order to calculate and simplify this product, we need to use the following properties:
[tex]\begin{gathered} \sqrt[]{a}\cdot\sqrt[]{b}=\sqrt[]{a\cdot b} \\ \sqrt[c]{a^b}=a\sqrt[c]{a^{b-c}} \end{gathered}[/tex]So we have that:
[tex]\begin{gathered} 3\sqrt[]{6}\cdot5\sqrt[]{12} \\ =(3\cdot5)\cdot(\sqrt[]{6}\cdot\sqrt[]{2\cdot6}) \\ =15\cdot\sqrt[]{2\cdot6^2} \\ =15\cdot6\cdot\sqrt[]{2} \\ =90\sqrt[]{2} \end{gathered}[/tex]So the result in the simplest radical form is 90√2.
help mee pleaseeeeeeeeeeeeee
Step-by-step explanation:
this simply means to put first 5, then 9 and then 12 in place of the x in the function and calculate the 3 results.
a.
after 5 years it is worth
V(5) = -1500×5 + 21000 = -7500 + 21000 = $13,500
b.
after 9 years it is worth
V(9) = -1500×9 + 21000 = -13500 + 21000 = $7,500
c.
V(12) = $3000
means that after 12 years the car is worth only $3000.
let's check
V(12) = -1500×12 + 21000 = -18000 + 21000 = $3000.
correct.
Which of the following shows a matrix and its inverse?
To find the inverse matrix, augment it with the identity matrix and perform row operations trying to make the identity matrix to the left. Then to the right will be the inverse matrix.
[tex]\mleft[\begin{array}{cc|cc}-2 & 1 & 1 & 0 \\ 0 & -3 & 0 & 1\end{array}\mright][/tex][tex]\begin{gathered} R_1=\frac{R_{1}}{2}\mleft[\begin{array}{cc|cc}1 & -\frac{1}{2} & \frac{1}{2} & 0 \\ 0 & -3 & 0 & 1\end{array}\mright] \\ R_2=\frac{R_{2}}{3}\mleft[\begin{array}{cc|cc}1 & -\frac{1}{2} & \frac{1}{2} & 0 \\ 0 & 1 & 0 & -\frac{1}{3}\end{array}\mright] \\ R_1=R_1+\frac{R_{2}}{2}\mleft[\begin{array}{cc|cc}1 & 0 & \frac{1}{2} & \frac{1}{6} \\ 0 & 1 & 0 & \frac{1}{3}\end{array}\mright] \end{gathered}[/tex]These corresponds to:
[tex]\mleft[\begin{array}{cc}2 & -1 \\ 0 & 3\end{array}\mright]\mleft[\begin{array}{cc}\frac{1}{2} & \frac{1}{6} \\ 0 & \frac{1}{3}\end{array}\mright][/tex]Which statements about the graph of the exponential function f(x) are TRUE?The x-intercept is 1.The y-intercept is 3.The asymptote is y = -3The range is all real numbers greater than -3The domain is all real numbers.f(x) is positive for all x-values greater than 1As x increases, f(x) approaches, but never reaches, -3.
1 The x-intercept is the value of x where the graph intersects the x-axis. The graph crosses the x-axis at x = 1. This statement is true.
2 The y-intercept is the value of y where the graph intersects the y-axis. The graph crosses the y-axis at y = -2. This statement is false.
3 The horizontal asymptote is the value of y to which the graph approaches but never reaches. This value seems to be y = -3, thus this statement is true.
4 The range is the set of values of y where the function exists. The graph exists only for values of y greater than -3. This statement is true.
5 We can give x any real value and the function exists, i.e., any vertical line would eventually intersect the graph. This statement is true.
To find the domain of a function when we are given the graph, we use the vertical line test. This consists of drawing an imaginary vertical line throughout the x-axis. If the line intersects the graph, that value of x is part of the domain.
This imaginary exercise gives us the centainty that there is no value of x that won't intercept the graph, thus the domain is the set of all the real values.
6 We can see the graph is positive exactly when the function has its x-intercept, thus This statement is true.
7 As x increases, y goes to infinity. The value of -3 is not a number where f(x) approaches when x increases, but when x decreases. This statement is false.
Which of the following functions is graphed below?
So, y is a system two distinct exponential functions.
The function on the bottom is a cubic function with a y-intercept of -3, and the full dot means that point is included in the domain.
y = x^3 - 3, x ≤ 2
The other function is a quadratic function with a currently unknown y-intercept. The hollow dot on point 2 means that the point is not included in the domain of the function.
y = x^2 + b, x > 2
So, given that there is only one option that matches this, even with the unknown b value, we know:
[tex]y = \left \{ {{x^3 - 3, x\leq 2} \atop {x^2 + 6, x > 2}} \right.[/tex]
So the answer is C.
Find the measure of angle CDB. Explain your reasoning, including the theorem or postulate you used. (2 pts.) b) Find the measure of angle. (1 pt.)
The triangle is isosceles, since two of its sides are equal. Besides, the little triangles ABD and CBD are congruent and this can be concluding using the criterion SSS , since they share one side, and the other sides are equal. Then the angles are congruent, and the angles ADB and CDB are congruent and have the same measure. Then
[tex]\begin{gathered} m\angle ADB+m\angle CDB=m\angle ADC \\ 2m\angle CDB=m\angle ADC \\ m\angle CDB=\frac{72}{2} \\ m\angle CDB=32 \end{gathered}[/tex]Then, the measure of angle CDB is 32 degrees.
Find the slope of the line passing through points -8, 8 and 7,8
We can calculate the slope of a line using the formula
[tex]m=\frac{y_b-y_a_{}}{x_b-x_a}[/tex]Let's say that
[tex]\begin{gathered} A=(-8,8) \\ B=(7,8) \end{gathered}[/tex]Therefore
[tex]\begin{gathered} x_a=-8,y_a=8 \\ x_b=7,y_b=8 \end{gathered}[/tex]Using the formula
[tex]m=\frac{y_b-y_a}{x_b-x_a}=\frac{8-8}{7-(-8)}=\frac{0}{15}=0[/tex]The slope of the line passing through points (-8, 8) and (7,8) is 0. Which means it's a constant function (horizontal line).
In 1980 approximately 4,825 million metric tons of carbon dioxide emissions were recorded for the United States. That number rose to approximately 6,000 million metric tons in the year 2005. Here you have measurements of carbon dioxide emissions for two moments in time. If you treat this information as two ordered pairs (x, y), you can use those two points to create a linear equation that helps you make predictions about the future of carbon dioxide emissions!A) Organize the measurements into ordered pairs. B) Find the slope,C) Set up an equation in point-slope form,D) Show the equation in slope-intercept form,E) Predict emissions for the year 2020,
ANSWER and EXPLANATION
A) To organize the measurements in ordered pairs implies that we want to put them in the form:
[tex](x_1,y_1);(x_2,y_2)[/tex]Therefore, the measurements in ordered pairs are:
[tex]\begin{gathered} (1980,4825) \\ (2005,6000) \end{gathered}[/tex]Note: 4825 and 6000 are in millions (10⁶) of metric tons
B) To find the slope, apply the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Therefore, the slope is:
[tex]\begin{gathered} m=\frac{6000-4825}{2005-1980} \\ m=\frac{1175}{25} \\ m=47\text{ million metric tons per year} \end{gathered}[/tex]C) To find the in point-slope form, we apply the formula:
[tex]y-y_1=m(x-x_1)_{}[/tex]Therefore, we have:
[tex]y-4825=47(x-1980)[/tex]Note: the unit is in million metric tons
D) To show the equation in point-slope form, we have to put it in the form:
[tex]y=mx+b[/tex]To do that, simplify the point-slope form of the equation:
[tex]\begin{gathered} y-4825=47(x-1980) \\ y=47x-93060+4825 \\ y=47x-88235 \end{gathered}[/tex]E) To predict the emissions for the year 2020, substitute 2020 for x in the equation above:
[tex]\begin{gathered} y=47(2020)-88235 \\ y=94940-88235 \\ y=6705\text{ million metric tons} \end{gathered}[/tex]That is the prediction for the year 2020.
has overdrawn his bank account Jim has overdrawn his bank account and has a balance of -$3.47.he received a paycheck of $292.54 he deposits $163.93 of his paycheck into his account how much does Jim have in his bank account after the deposit is made
Since Jim deposits $ 163.93 of his paycheck into his account and there has a balance of - $ 3.47, then he has in his account:
[tex]\text{\$}$163.93$-\text{\$}3.47=\text{ \$}160.46[/tex]Therefore, Jim has $ 160.46 in his bank account after the deposit is made.
A baker has 85 cups of flour to make bread. She uses 6 1/4 cups of flour for each loaf of bread. How many loaf of bread can she make
Answer;
The number of loaf of bread she can make is;
[tex]13\text{ loaves}[/tex]Explanation:
Given that a baker has 85 cups of flour to make bread.
[tex]A=85\text{ cups}[/tex]And for each bread she uses 6 1/4 cups of flour.
[tex]r=6\frac{1}{4}\text{ cups}[/tex]The number of loaf of bread she can make can be calculated by dividing the total amount of flour by the amount of flour per bread;
[tex]\begin{gathered} n=\frac{A}{r}=\frac{85}{6\frac{1}{4}}=\frac{85}{6.25} \\ n=13.6 \end{gathered}[/tex]Since it will not complete the 14th loaf of bread.
So, the number of loaf of bread she can make is;
[tex]13\text{ loaves}[/tex]5000 + 300 + 8 in standard form
The given arithmetic expression is:
5000 + 300 + 8
This sum can be computed as shown below:
Therefore, 5000 + 300 + 8 = 5308
Convert 5308 to standard form
[tex]5308\text{ = 5.308 }\times10^3[/tex]
12. Find DC.
A
20
54°
B
D
28°
C
The measure of the DC is 30.43 units after applying the trigonometric ratios in the right-angle triangle.
What is the triangle?In terms of geometry, a triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.
It is given that:
A triangle is shown in the picture.
From the figure:
Applying sin ratio in triangle ADB
sin54 = BD/20
BD = 20sin54
BD = 16.18
Applying the tan ratio in triangle CDB
tan28 = 16.18/DC
DC = 30.43 units
Thus, the measure of the DC is 30.43 units after applying the trigonometric ratios in the right-angle triangle.
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Which expression simplifies to 5. A. 27/3 - 14. B. 27/3+4. C. -27/3-4. D. -27/3+14
4 Consider the quadratic equation below.[tex]4 {x}^{2} - 5 = 3x + 4[/tex] Determine the correct set-up for solving the equation using the quadratic formula.
The equation:
4x² - 5 = 3x + 4
First, we need to re-arrange in the form : ax² + bx + c
4x² - 5 = 3x + 4
4x² - 3x -5 -4 = 0
4x² - 3x -9 =0
comparing the above with ax² + bx + c
a= 4 b= -3 c=-9
we will then substitute the values into the quadratic formula:
[tex]x\text{ = }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex][tex]x=\frac{-(-3)\pm\sqrt[]{(-3)^2-4(4)(-9)}}{2(4)}[/tex]A person has 29 1/2 -yd of material available to make a doll outfit. Each outfit requires 3/4 yd of material. a. How many outfits can be made? b. How much material will be left over?
If f(x) = sin(x ^ 5) , find f^ prime (x)
Solution
Step 1
Write the function.
[tex]f(x)\text{ = sin\lparen x}^5)[/tex]Step 2
Use the chain rule to find f'(x)
[tex]\begin{gathered} f^{\prime}(x)\text{ = }\frac{df}{du}\times\frac{du}{dx} \\ \\ u\text{ = x}^5 \\ \\ \frac{du}{dx}\text{ = 5x}^4 \\ f(x)\text{ = sinu} \\ \\ \frac{df}{du}\text{ = cosu} \end{gathered}[/tex]Step 3
[tex]\begin{gathered} f^{\prime}(x)\text{ = 5x}^4\text{ }\times\text{ cosu} \\ \\ f^{\prime}(x)\text{ = 5x}^4cos(x^5) \end{gathered}[/tex]Step 4
Substitute x = 4 to find f'(4).
[tex]\begin{gathered} f^{\prime}(4)\text{ = 5}\times4^4\times cos(4^5) \\ \\ f^{\prime}(4)=\text{ 1280}\times cos1024 \\ \\ f^{\prime}(x)\text{ = 715.8} \end{gathered}[/tex]Final answer
I need help with math. I have a big exam coming up but I do t understand this lesson at all. Can I have help answering all the questions?
Step 1
Given;
[tex]\begin{gathered} Head\text{ represent male} \\ Tail\text{ represent female} \end{gathered}[/tex]The total number of puppies is 4 represented by 4 coins.
Step 2
Find the experimental probability that exactly 3 of the puppies will be female
[tex]\begin{gathered} From\text{ table we find that THTT, TTHT, HTTT and HTTT are the only outcomes that } \\ \text{show exactly 3 females} \\ Remember\text{ tail\lparen t\rparen is for female puppies} \end{gathered}[/tex]Therefore, the total number of samples/coin tosses=20
The formula for probability is;
[tex]Pr\left(event\right)=\frac{Numberofrequiredevent}{Total\text{ number of events}}[/tex]Total number of events =the total number of samples/coin tosses=20
Number of required events= outcomes with 3 T's from the tab;e=4
Hence.
[tex]=\frac{4}{20}=0.2=0.2\times100=20\text{\%}[/tex]Answer;
[tex]\frac{4}{20}=0.20=20\text{\%}[/tex]how do I solve (4w+3x+5)-(4w-3x+2)
Answer:
6x + 3
Explanation:
To solve the initial expression, we need to write it without the parenthesis as:
( 4w + 3x + 5 ) - ( 4w - 3x + 2)
4w + 3x + 5 - 4w + 3x - 2
Then, we need to identify the like terms as:
4w and -4w are like terms
3x and 3x are like terms
5 and -2 are like terms
Now, we can organize the terms as:
4w - 4w + 3x + 3x + 5 - 2
Adding like terms, we get:
(4w - 4w) + (3x + 3x) + (5 - 2)
0 + 6x + 3
6x + 3
Therefore, the answer is 6x + 3
find the equation of the line?
Let's calculate the straight line equation
To do this we will take two points from the graph
A = (0,3)
B= (2,0)
For them we will first calculate the slope of the curve
[tex]m=\frac{y2-y1}{x2-x1}[/tex][tex]\begin{gathered} m=\frac{0-3}{2-0} \\ m=\frac{-3}{2} \end{gathered}[/tex]Now let's calculate the y-axis intersection
[tex]\begin{gathered} b=y-mx \\ b=3-m\cdot0 \\ b=3 \end{gathered}[/tex]The equation of the line in the slope-intercept form is
[tex]y=-\frac{3}{2}x+3[/tex]Which of these tables doesn't show a proportional relationship? MY 2 B 4 12. 18 X 1 2 2 4 3 6 X Y 0 - 2 1 에 1 2 4 X Y 0 0 1 1 2 2
Answer:
The third table.
Explanation:
In a proportional relationship, the and y values are in a constant ratio.
system by applications i belive the answer is A can you check?
Let's use the variable x to represent the cost of a senior ticket and y to represent the cost of a child ticket.
If the cost of 1 senior ticket and 1 child ticket is $18, we have:
[tex]x+y=18[/tex]If 2 senior tickets and 1 child tickets cost $27, we have:
[tex]2x+y=27[/tex]Subtracting the first equation from the second one, we can solve the result for x:
[tex]\begin{gathered} 2x+y-(x+y)=27-18 \\ 2x+y-x-y=9 \\ x=9 \end{gathered}[/tex]Now, solving for y:
[tex]\begin{gathered} x+y=18 \\ 9+y=18 \\ y=18-9 \\ y=9 \end{gathered}[/tex]Therefore the cost of one senior ticket is $9 and the cost of one child ticket is $9.
Correct option: D.
A random sample of 41 people is taken. What is the probability that the main IQ score of people in the sample is less than 99? Round your answer to four decimal places if necessary(See picture )
Solution:
Given:
[tex]\begin{gathered} \mu=100 \\ \sigma=15 \\ n=41 \\ x=99 \end{gathered}[/tex]From the Z-scores formula;
[tex]\begin{gathered} Z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}} \\ Z=\frac{99-100}{\frac{15}{\sqrt{41}}} \\ Z=-0.42687494916 \\ Z\approx-0.4269 \end{gathered}[/tex]From Z-scores table, the probability that the mean IQ score of people in the sample is less than 99 is;
[tex]\begin{gathered} P(xTherefore, to 4 decimal places, the probability that the mean IQ score of people in the sample is less than 99 is 0.3347
Space shuttle astronauts each consume an average of 3000 calories per day. One meal normally consists of a main dish, a vegetable dish, and two different desserts. The astronauts can choose from 11 main dishes, 7 vegetable dishes, and 12 desserts. How many different meals are possible?
Okay, here we have this:
Considering the provided information, we are going to calculate how many different meals are possible, so we obtain the following:
There are 11 ways to choose a main dish, 7 ways to choose a vegetable, 12 ways to choose the first dessert, and 11 ways to choose the second dessert. Then:
We multiply to find the possible number of combinations:
[tex]\begin{gathered} 11\cdot7\cdot12\cdot11 \\ =10164 \end{gathered}[/tex]Finally we obtain that there are 10164 different meals possible.
Subtract the following polynomials 1) (2x + 43) - (-3x-9)2) (f+9) - (12f 79)3) (75 X²)+ 23 + 13) - (15 X² - X + 40)
for 1.
2x+43+3x+9=5x+52
2.
f+9-12f+9=f-12f+9-9=-11f
3.
75x^2 +23x+13-15x^2+x-40=
=60x^2+24x-27
for 2)
23d^3+(7g^9)^13
remember that power to the power means that you need to multipy the exponents
=23d^3+7^13g^117
34x(2x-11)=68x^2-374x
2m(m+3n)=2 m^2+6mn
we have lenght
l=2x+5
w=x+7
area, A= lxw
A= (2x+5)(x+7)
this is the polynomial for the area
if we have x=12
l= (2*12)+5=24+5=29
w=12+7=19
A=29*19=551 ft^2
Write an equation in the form r(x) = p(x) / q(x) for each function shown below.Pls see pic for details
c.
The line equation is of the form
[tex]y=mx+c\ldots(1)[/tex]From the graph, we observe and find these points
(1,5) and (0,4) lie on the given line.
Substituting x=1, y=5 in equation (1), we get
[tex]5=m(1)+c[/tex][tex]m+c=5\ldots\text{.}(2)[/tex]Substituting x=0, y=4 in equation (1), we get
[tex]4=m(0)+c[/tex][tex]c=4[/tex]Substituting c=4 in equation (2), we get
[tex]m+4=5[/tex][tex]m=5-4[/tex][tex]m=1[/tex]Substituting c=4,m=1 in equation (1), we get
[tex]y=x+5[/tex]We need to write this equation in the form of r(x) = p(x) / q(x).
[tex]r(x)=\frac{p(x)}{q(x)}\ldots(3)[/tex]Let r(x)=x+5, q(x)=x, and subsitute in the equation , we get
[tex]x+5=\frac{p(x)}{x}[/tex]Using the cross-product method, we get
[tex]x(x+5)=p(x)[/tex][tex]x\times x+x\times5=p(x)[/tex][tex]x^2+5x=p(x)[/tex]Substitute values in equation (3), we get
[tex]x+5=\frac{x^2+5x}{x}[/tex]Hence the required equation is
[tex]x+5=\frac{x^2+5x}{x}[/tex]Text-to-Speech 11. Diva wants to make a flower arrangement for her aunt's birthday. She wants 1/3 of the arrangement to be roses. She has 12 roses. How many other flowers does she need to finish the arrangement?
HELP PLEASE!!!!!!!!!!! ILL MARK BRAINLIEST
The rational number - 91 / 200 is a number between the decimal numbers - 0.45 and - 0.46.
How to determine a rational number between two decimal numbers
In this problem we find two decimal numbers, of which we need to find a rational number between these numbers. Please notice that the decimal numbers are also rational numbers. First, we transform each decimal number into rational numbers:
- 0.45 = - 45 / 100
- 0.46 = - 46 / 100
Second, find a possible rational number between the two ends by the midpoint formula:
x = (1 / 2) · (- 45 / 100) + (1 / 2) · (- 46 / 100)
x = - 45 / 200 - 46 / 200
x = - 91 / 200
Then, the rational number - 91 / 200 is a number between - 0.45 and - 0.46.
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