Answer:
21
Step-by-step explanation:
The length of the other leg (x) is 12 cm.
We have,
To find the length of the other leg, we can use the Pythagorean theorem.
Using this theorem, we can set up the following equation:
x² + 5² = 13²
Simplifying the equation:
x² + 25 = 169
Subtracting 25 from both sides:
x² = 144
Taking the square root of both sides:
x = ±12
Since length cannot be negative in this context, the length of the other leg (x) is 12 cm.
Thus,
The length of the other leg (x) is 12 cm.
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The complete question:
In a right triangle, the length of one of the legs is 5 cm, and the length of the hypotenuse is 13 cm.
What is the length of the other leg, represented as x?
In the diagram, each shape has a value and the sums of the shapes in each of the first three rows is given. Find the sum of the shapes in the fourth row.
Answer:
26
Step-by-step explanation:
2 squares + 3 circles = 31. So, the sum of the squares is divisible by two, and the sum of the circles is divisible by 3. Then, I used trial and error to figure out that the square's value is five, and the circle's value is seven. 5 + 7 + 7 = 19. 27 - 19 = 8. The triangle's value is eight. 5 + 7 + 12 = 24. It works. 15 + 7 + 4 = 26
Answer:
26
Step-by-step explanation:
i did it i got it correct!!!
This dot plot is not symmetric, and the data set has two
extreme values.
1 2 3 4
6 7 8 9 10
What is the best measure of center for this dot plot?
O A. The interquartile range (IQR)
O B. The mean
O C. The mean absolute deviation (MAD)
O D. The median
Answer:
D
Step-by-step explanation:
In a sample of 1000 cases, the mean of a certain test is 14 and the standard deviation is 2.5. Assume the distribution to be normal. The top 20% of the students will score how many points above the mean
Answer:
The top 20% of the students will score at least 2.1 points above the mean.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
The mean of a certain test is 14 and the standard deviation is 2.5.
This means that \(\mu = 14, \sigma = 2.5\)
The top 20% of the students will score how many points above the mean
Their score is the 100 - 20 = 80th percentile, which is X when Z has a pvalue of 0.8. So X when Z = 0.84.
Their score is:
\(Z = \frac{X - \mu}{\sigma}\)
\(0.84 = \frac{X - 14}{2.5}\)
\(X - 14 = 0.84*2.5\)
\(X = 16.1\)
16.1 - 14 = 2.1
The top 20% of the students will score at least 2.1 points above the mean.
jacob said the product of 8/9 and 2 and 3/4 is 3 and 1/4. how can you tell that his answer is wrong?
Answer:
he is wrong becuase 89 times a number greater than 0 cannot result in a product greater than the number
Step-by-step explanation:
Based on real algebra properties, we know that the product of 8/9 and 2 and 3/4 is not 3 and 1/4.
How to infer the correctness of a product?The multiplication of two positive integers equals another positive integer. Each term of a multiplication can be rewritten as sums of multiples of 10, which can be simplified by algebra:
Given; Definition of multiplication
8/9 and 2 = 26/9
3/4
The product is;
26/9 x 3/4
= 13 x 1/6
= 13/6
Based on real algebra properties, we know that the product of 8/9 and 2 and 3/4 is not 3 and 1/4.
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4x=2y-9 plus -8x+6y=6
Answer:
-4x+4y+3=0
Step-by-step explanation:
(4x-2y+9=0)+(-8x+6y-6=0)
Add like terms:
-4x+4y+3=0
A committee of four people is formed by selecting members from a list of 12 people.
How many different committees can be formed?
__ committees
The number of different committees that can be formed is 495
How many different committees can be formed?From the question, we have the following parameters that can be used in our computation:
People = 12
Committee = 4
These can be represented as
n = 12 and r = 4
The number of different committees that can be formed is
Number = nCr
So, we have
Number = 12C4
Evaluate
Number = 495
Hence, the committee are 495
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Draw the image of the following segment after a dilation centered at the origin with a scale factor of 2.
The length of the line segment after the dilation with a scale factor of 2 is given by the equation A' = L ( 2 ) , where L is the length of the segment
What is Dilation?Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent
Given data ,
Let the length of the line segment be represented as L
Now , the dilation factor is represented as d = 2
And , the dilation centered at the origin
So , the length of the line segment after the dilation is A'
On simplifying the equation , we get
The length of the line segment after the dilation A' = L x ( dilation factor )
The length of the line segment after the dilation A' = L ( 2 )
Hence , the dilation A' = 2L
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A bride is choosing a dress for her bridesmaids. If there are 4 styles, 7 colors, and 5 fabrics, in how many ways can she select the bridesmaids' dress?
Answer: 60
Step-by-step explanation: multiply 4,7,and 5
She can select the bridesmaids' dress in 140 possible ways.
What is Permutation?Permutation represents each of the several possible ways in which a set or number of things can be ordered or arranged.
Given is a bride who is choosing a dress for her bridesmaids which are available in 4 styles, 7 colors, and 5 fabrics.
Now, for every possible style there exist a dress for that color. So, with 4 styles and 7 colors, the total number of possible dresses will be = 7 x 4 = 28. Now, for these 28 dresses, their are 5 different fabric available, so the total number of possible ways or dresses from which she can select the dress are = 28 x 5 = 140
Therefore, she can select the bridesmaids' dress in 140 possible ways.
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What is a correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9?
–12 – 20x ≤ –6x + 9
–12 – 20x ≥ –6x + 9
–12 + 20x ≤ –6x + 9
–12 + 20x ≥ –6x + 9
Answer:
-12 + 20x ≥ -6x + 9
Fourth choice
Step-by-step explanation:
Inequalities
We are given the inequality:
-4(3 - 5x) ≥ -6x + 9
Solving the inequality implies having x isolated on one of the sides.
We must start by removing the parentheses. It will be done by multiplying -4 by (3 - 5x). Since this operation doesn't imply multiplying all the inequality by a negative number, the sign won't be flipped:
-4*3 - (-4)5x ≥ -6x + 9
Multiplying:
-12 + 20x ≥ -6x + 9
Fourth choice
pls help I'll mark brainliest
.38, .37, and .36 are all less than 1
A circle with a centre 0, has an equation x2 + y2 = 25
The coordinate A (4,3) is on the circumference of the circle.
Find the equation of the tangent at point A.
The linear equation of the tangent at point A is given by:
\(y = \frac{-4x + 25}{3}\)
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, to find the slope, we need to find the derivative at (4,3), using implicit differentiation. Hence:
\(2x\frac{dx}{dx} + 2y\frac{dy}{dx} = 0\)
\(\frac{dy}{dx} = -\frac{x}{y}\)
\(\frac{dy}{dx} = -\frac{4}{3}\)
Then:
\(y = -\frac{4}{3}x + b\)
We use point (4,3) to find b, hence:
\(y = -\frac{4}{3}x + b\)
\(3 = -\frac{16}{3} + b\)
\(b = \frac{25}{3}\)
Hence, the equation is:
\(y = \frac{-4x + 25}{3}\)
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IS THIS CORRECT? THANK YOU
Answer:
yes its correct
Step-by-step explanation:
YES
I GOT THE POWER OF GOD AND ANIME ON MY SIDE
In 1990, tests showed that water in a lake was polluted with 7 milligrams of mercury compounds per 1000 liters of water. Cleaning up the lake became an immediate priority, and environmentalists determined that the pollution level would drop at the rate of 0.75 milligrams of mercury compounds per 1000 liters of water per year if all of their recommendations were followed. If 1990 corresponds to x = 0, find the equation of the line that allows the environmentalists to predict the pollution level y in future years if their recommendations are followed. Sketch the graph of the equation and determine when the lake will be free of mercury pollution according to this graph.
Answer:
Step-by-step explanation:
First, we need to make the Equation
As the rate of change in mercury compound per year is 0.75 mg per thousand liter, So
m = -0.75
Equation of the line will be as follow
y = -0.75x + c
In 1990
x = 0
Y( 0 ) = 7
Placing values in the equation
7 = -0.75 (0) + c
7 = c
Now the Equation will be as follow
y = 0.75x + 7
Grasph is attached with this asnwer please find it.
Sundeep mixed 300 mL of water with 100 mL of sugar. She says "the total volume is
300 mL + 100 mL = 400 mL." Do you agree with Sundeep? Explain why or why not.
No, I don't agree with Sundeep. The mixture wont simply add up
How to show the volume will not be 400 mlWhen two liquids are mixed together, their volumes don't simply add up to equal the total volume of the mixture.
When sugar is mixed with water, the total volume of the mixture is usually slightly greater than the volume of the water alone, because the sugar particles take up space between the water molecules.
The volume of the mixture will be equal to the sum of the individual volumes only if the two liquids are completely immiscible, meaning they don't mix together at all. In this case, the total volume of the mixture will be equal to the sum of the volumes of water and sugar, which is 400 mL.
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4 in.
3 in.
2 in.
2 in.
6 in.
Find the surface area.
square inches
(Hint: The rectangular faces
are different sizes.)
Answer:
The correct answer is 5in
Step-by-step explanation:
6+4=10÷2=5in
Find the length of DC.
Answer:
sqart(89) in
Step-by-step explanation:
As triangle ABC is a right triangle, so sqrt(5^2 + 8^2) = sqrt(89) approximately 9.43 in.
PLS HURRY I AM GIVING BRAINLIEST!!!
the question is in the photo!!
Jordan spend 25 minutes writing each dayNoHow much time does Jordan spend writing each dayFrom the question, we have the following parameters that can be used in our computation:D + W = 75W + 25 = DSo, we haveW + W + 25 = 75EvaluateW = 25This means that Jordan spends 25 minutes on writing is it possible?Based on the answer in (a), the truth statement is No
Please help me with this
An example of a function that models a linear relationship between two quantities, x and y is y = mx + b
How to explain the functionWe need to use the equation of a straight line, which is commonly expressed in slope-intercept form as:
y = mx + b
In this function, x represents the independent variable, m is the slope of the line, and b is the y-intercept. To use this function, we simply plug in the values of x, m, and b that correspond to the specific relationship we are modeling.
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Who was in command of the Texan forces at the Alamo
Travis' famous letter, addressed to "The People of Texas and All Americans in the World," in which he passionately appealed for reinforcements and vowed to "never surrender or retreat," has become a symbol of the fortitude and sacrifice displayed by the Texan defenders at the Alamo.
The commander of the Texan forces at the Alamo during the famous battle in 1836 was Colonel William B. Travis. Travis, a lawyer and soldier, was chosen as the leader of the Texan garrison at the Alamo, a former mission turned fortress in San Antonio, Texas. He assumed command of the Texan forces in early 1836 and played a crucial role in the defense of the Alamo against the Mexican army led by General Santa Anna.
Travis and his men, along with notable figures such as James Bowie and Davy Crockett, bravely defended the Alamo against overwhelming odds for thirteen days. Despite their courage and determination, the Texan defenders were ultimately overrun by the Mexican forces on March 6, 1836, and suffered heavy casualties, including the deaths of Travis, Bowie, and Crockett.
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Two angles of a triangle have the same measure and the third one is 9 degrees greater than the measure of each of the other two. Find the measure of the LARGEST angle in the triangle.
Answer: The LARGEST angle has a measure of
degrees.
The largest angle of the triangle is ∠C = 66°
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ΔABC
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
Now , the measure of ∠A = measure of ∠B = x
And , the measure of ∠C = measure of ∠A + 9°
Substituting the values in the equation , we get
x + x + ( x + 9 ) = 180
On simplifying the equation , we get
3x + 9 = 180
Subtracting 9 on both sides of the equation , we get
3x = 171
Divide by 3 on both sides of the equation , we get
x = 57°
So , the measure of ∠A = 57°
Now , the measure of ∠C = 57 + 9 = 66°
Hence , the measure of ∠C of triangle is 66°
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A box has the shape of a rectangular prism with height 28 cm. If the height is increased by 0.2cm, by how much does the surface area of the box increase? L=13 W=8.7 H=28
The surface area of the box increases by 27.4 cm² when the height is increased by 0.2 cm.
To find the increase in surface area, we first need to calculate the initial surface area of the box and then calculate the surface area after increasing the height.
The formula for the surface area of a rectangular prism is given by:
Surface Area = 2*(length width + length height + width*height)
Initial Surface Area:
Length (L) = 13 cm
Width (W) = 8.7 cm
Height (H) = 28 cm
Initial Surface Area = 2*(138.7 + 1328 + 8.7*28)
Next, we calculate the new surface area after increasing the height by 0.2 cm. The new height is:
New Height = Initial Height + Increase in Height = 28 cm + 0.2 cm
New Surface Area = 2*(138.7 + 13(28+0.2) + 8.7*(28+0.2))
To find the increase in surface area, we subtract the initial surface area from the new surface area:
Increase in Surface Area = New Surface Area - Initial Surface Area
Let's calculate the values:
Initial Surface Area = 2*(138.7 + 1328 + 8.728) = 2(113.1 + 364 + 243.6) = 2*(720.7) = 1441.4 cm²
New Surface Area = 2*(138.7 + 13(28+0.2) + 8.7*(28+0.2)) = 2*(113.1 + 377.2 + 244.1) = 2*(734.4) = 1468.8 cm²
Increase in Surface Area = New Surface Area - Initial Surface Area = 1468.8 cm² - 1441.4 cm² = 27.4 cm²
Therefore, the surface area of the box increases by 27.4 cm² when the height is increased by 0.2 cm.
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Fill in the table using this function rule.
f(x) = √√x+6
Simplify your answers as much as possible.
Click "Not a real number" if applicable.
The table of values for the function rule y = √(x + 6) is
x | f(x)
-15 | Not a real number
6 | 0
19 | 5
75 | 9
How to complete the table of valuesFrom the question, we have the following parameters that can be used in our computation:
y = √(x + 6)
To fill in a table using a function rule, we apply the function rule to each input to calculate the corresponding output, and write these values in the right-hand column of the table
We have the x values to be
x = -15, -6, 19 and 75
Substitute the known values in the above equation, so, we have the following representation
y = √(-15 + 6) = Not a real number
y = √(-6 + 6) = 0
y = √(19 + 6) = 5
y = √(75 + 6) = 9
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the standard form of a quadratic equation is ax^2+bc+c=0 identify the values of a,b and c in the quadratic equation 2x^2-5x+4=8x-6 with a>0
Answer:
a = 2, b = -13 and c = 10
Step-by-step explanation:
The given quadratic equation, 2x^2-5x+4=8x-6, must be rewritten in standard form before a, b and c can be identified.
Combining like terms in 2x^2-5x+4=8x-6, we get:
2x^2 - 13x + 10
Then a = 2, b = -13 and c = 10.
At the Madison Ski Resort, it snowed 5 feet yesterday and 2/3 of a foot today. How much more did it snow yesterday than today?
Write your answer as a fraction or as a whole or mixed number.
Answer:
4 1/3
Step-by-step explanation:
this is just a subtraction problem. What you know is that it snowed 5ft yesterday and 2/3ft today. So that means that the amount of more snow yesterday can be calculated with 5 - 2/3ft (this will show how much more snow there was yesterday). The result of this expression would be 4 1/3. Hope this helps!
ryann has 80$ to spend on gifts. She already decided to use $25 for a scarf for her grandmother. She wants to spend the reaming money to purchase gifts for her four freinds. She will spend the same amount of money for each friend's gift. What is the most she can spend on each friend?
Answer:
Okay so since she has 80 dollars, and already spent 25, then she would have 55 dollars remaining.
Now that she has 55 dollars, she will divide it up evenly between her 4 friends.
55/4 = 13.75
The most that she would be able to give them is $13.75
Step-by-step explanation:
Hope it helps! =D
PLEASE HELP ME
A pyramid has a row of 100 blocks in the first row, 96 blocks in the
second row, and 92 blocks in the third row. (A) Write an explicit rule to
model the number of blocks in the nth row of the pyramid. (B) Use the rule
to find how many blocks are in the 17th row.
Answer:
3196
Step-by-step explanation:
A. You Add all the blocks.
B. Then you multiply 17 x your answer then you get your answer.
-8+r>-8
please show work
Hello there!
-8+r>-8
Move all the numbers to the right:
r>-8+8
r>0
Hope it helps!
~Just a joyful teen
\(GraceRosalia\)
In a sample of 560 adults, 336 had children. Construct a 95% confidence interval for the true population proportion of adults with children.
Give your answers as decimals, to three places
< p <
What is the expected value of �?
The confidence interval is 0.559 < p < 0.641 and expected value is 0.600
Confidence IntervalTo construct a confidence interval for the true population proportion, we can use the formula:
p ± Z * √((p × (1 - p)) / n)
Where:
p = sample proportion (336/560)
Z = critical value for the desired confidence level
95% confidence = Z-value of approximately 1.96
n = 560
Let's calculate the confidence interval:
p = 336/560 ≈ 0.600
Z ≈ 1.96 (for a 95% confidence level)
n = 560
Plugging these values into the formula:
p ± Z × √((p × (1 - p)) / n)
0.600 ± 1.96 × √((0.600 × (1 - 0.600)) / 560)
0.600 ± 1.96 × √((0.240) / 560)
0.600 ± 1.96 × √(0.0004285714)
0.600 ± 1.96 × 0.020709611
0.600 ± 0.040564459
The confidence interval is:
0.559 < p < 0.641
Therefore, the 95% confidence interval for the true population proportion of adults with children is 0.559 < p < 0.641.
The expected valueFor proportions, the expected value is simply the sample proportion, which is approximately 0.600.
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Afiq. Bala and Chin played a game of marbles. Before the game, Bala had fewer marbles than Afig and Chinhad?
- as many marbles as Bala.
After the game, Balahad lost 20% of his marbles to Chinwhile Afig had lost
3
of his marbles to Chin. Chingained 105 marbles at the end of the
game.
(a)How many marbles didChinhave after the game?
(b)After the game, the 3 children each bought another 40 marbles. How manymarbles did the 3 children have altogether?
(a) Chin had 93.1 marbles after the game.
(b) The three children had a total of 271.44 marbles altogether.
Let's break down the problem step by step to find the answers:
Initial marbles
Before the game:
Let's assume Afiq had x marbles.
Bala had 1/6 fewer marbles than Afiq, so Bala had (x - 1/6x) marbles.
Chin had 3/5 as many marbles as Bala, so Chin had (3/5)(x - 1/6x) marbles.
After the game
After the game, Bala lost 20% of his marbles to Chin, so he has 80% (or 0.8) of his initial marbles remaining.
Afiq lost 2/3 of his marbles to Chin, so he has 1/3 (or 0.33) of his initial marbles remaining.
Calculating the marbles
(a) How many marbles did Chin have after the game?
To find Chin's marbles after the game, we add the marbles gained from Bala to Chin's initial marbles and the marbles gained from Afiq to Chin's initial marbles.
Chin's marbles = Initial marbles + Marbles gained from Bala + Marbles gained from Afiq
Chin's marbles = (3/5)(x - 1/6x) + 0.8(x - 1/6x) + 0.33x
Chin's marbles = (3/5)(5x/6) + 0.8(5x/6) + 0.33x
Chin's marbles = (3/6)x + (4/6)x + 0.33x
Chin's marbles = (7/6)x + 0.33x
We are given that Chin gained 105 marbles, so we can equate the equation above to 105 and solve for x:
(7/6)x + 0.33x = 105
(7x + 2x) / 6 = 105
9x / 6 = 105
9x = 105 * 6
x = (105 * 6) / 9
x = 70
Substituting the value of x back into the equation for Chin's marbles:
Chin's marbles = (7/6)(70) + 0.33(70)
Chin's marbles = 10(7) + 0.33(70)
Chin's marbles = 70 + 23.1
Chin's marbles ≈ 93.1
Therefore, Chin had approximately 93.1 marbles after the game.
(b) After the game, the 3 children each bought another 40 marbles. To find the total number of marbles the 3 children have altogether, we need to sum up their marbles after the game and the additional 40 marbles for each.
Total marbles = Afiq's marbles + Bala's marbles + Chin's marbles + Additional marbles
Total marbles = 0.33x + 0.8(x - 1/6x) + (7/6)x + 40 + 40 + 40
Total marbles = 0.33(70) + 0.8(70 - 1/6(70)) + (7/6)(70) + 120
Total marbles = 23.1 + 0.8(70 - 11.7) + 81.7 + 120
Total marbles = 23.1 + 0.8 × 58.3 + 201.7
Total marbles = 23.1 + 46.64 + 201.7
Total marbles = 271.44
The three children had a total of 271.44 marbles altogether.
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Question
Afiq. Bala and Chin played a game of marbles. Before the game, Bala had 1/ 6 fewer marbles than Afig and Chinhad 3/5 as many marbles as Bala.
After the game, Balahad lost 20% of his marbles to Chinwhile Afig had lost
2/3 of his marbles to Chin. Chingained 105 marbles at the end of the
game.
(a)How many marbles didChinhave after the game?
(b)After the game, the 3 children each bought another 40 marbles. How manymarbles did the 3 children have altogether?
hope anyone help me please
Answer:
<
<
>
<
>
Step-by-step explanation:
-12<-4
-15<-2
-7>-29
0<20
-101>-159
Answer:
(a) (-8)+(-4) < (-8)-(-4)
(b) (-3)+7-(19) < 15-8+(-9)
(c) 23-41+Il > 23-41-11
(d) 39+(-24)-(15) < 36+(-52)-(-36)
(e)-231+79+51 >-399+159+81
note:
-1 is greater than-20