Answer:
x = √65
Step-by-step explanation:
You are given a right triangle with leg lengths 4 and 7, and you are asked for the length of the hypotenuse, x.
Pythagorean theoremThe Pythagorean theorem relates the lengths of the sides of a right triangle. It tells you the square of the hypotenuse (x²) is the sum of the squares of the other two sides.
x² = 4² +7² . . . . . . . . . Pythagorean relation
x² = 16 +49 = 65 . . . evaluate the expression
x = √65 . . . . . . . . . . take the square root
Can someone help with this question?✨
Step-by-step explanation:
it is the standard
y = abs(x)
function moved down by 2 units and moved right by 2 units.
to move it down by 2 units :
y = abs(x) - 2
and to move it right by 2 units :
y = abs(x - 2)
together, that is our requested function expression :
y = abs(x - 2) - 2
Can someone help me
Answer:
Slope=m=5/4
Point through which line is passing is (X,Y)=(4,−1)
By using slope-point form, the equation of line is given as,
(y−Y)=m(x−X)
(y−(−1))=5/4(x−4)
(y+1)=5x/4−5
(y+1)=(5x−20)/4
4(y+1)=5x−20
4y+4=5x−20
5x−4y−20−4=0
5x−4y−24=0
is the equation of line passing through the point (4,−1)and having slope 5/4
Hope it helps you :)
Step-by-step explanation:
Show your work please help me it’s due tomorrow!!!!
Answer: Consider me the brainiest. The answer is... Decimal form =4.083
Exact form= 49/12
The mixed number form=4 1/12
How do we solve fractions step by step?
Conversion a mixed number 2 1/3 to a improper fraction: 2 1/3 = 2 1/3 = 2 3 + 1/3 = 6 + 1/3 = 7/3
To find a new numerator
A; Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/3 = 6/3
b) Add the answer from the previous step 6 to the numerator 1. The new numerator is 6 + 1 = 7
c) Write a previous answer (new numerator 7) over the denominator 3.
Two and one-third are seven-thirds.
Conversion a mixed number 1 3/4 to a improper fraction: 1 3/4 = 1 3/4 = 1 · 4 + 3/4 = 4 + 3/4 = 7/4
To find a new numerator:
a) Multiply the whole number 1 by the denominator 4. Whole number 1 equally 1 * 4/4 = 4/4
b) Add the answer from the previous step 4 to the numerator 3. The new numerator is 4 + 3 = 7
c) Write a previous answer (new numerator 7) over the denominator 4. One and three quarters are seven quarters.
Add: 7/3 + 7/4 = 7 · 4/3 · 4 + 7 · 3/4 · 3 = 28/12 + 21/12 = 28 + 21/12 = 49/12 It
is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(3, 4) = 12. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 4 = 12. In the following intermediate step, it cannot further simplify the fraction result by cancelling. In other words - seven thirds plus seven quarters is forty-nine twelfths.
divide 0.08 ÷4.96 it will
We have to divide 0.08 by 4.96.
As both are decimals, we will multiply the numerator, 0.08, by tens until it becomes a whole number.
In this case, we have to multiply it 2 times:
\(0.08\cdot10\cdot10=0.8\cdot10=8\)Now we have to multiply the denominator the same amount of times (2):
\(4.96\cdot10\cdot10=49.60\cdot10=496\)Then, we have:
\(\frac{0.08}{4.96}=\frac{8}{496}\)Now we can write the division as:
Answer: Calculated to 3 decimal places, 0.08/4.96 = 0.016.
Question 8(Multiple Choice Worth 2 points)
(Writing Two-Step Equations MC)
A new gaming chair costs $455.95. You have already saved $155.95 and earn $37.50 each week babysitting. Write and solve an equation to determine how many weeks, w, you must babysit to earn enough money to buy the new gaming chair.
37.5 + 155.95w = 455.95; w = 8
37.5w + 155.95 = 455.95; w = 8
37.5w − 155.95 = 455.95; w = 16
37.5w − 455.95 = 155.95; w = 16
37.5w + 155.95 = 455.95; where w = 8; signifies the number of weeks required to babysit the business in order to purchase the gaming chair.
How do equations work?A mathematical formula that connects two expressions with the equals sign (=) expresses the equality of the two expressions. For instance, in English, an equation is any properly stated formula that consists of two expressions linked by the equals sign, whereas in French, an equation is described as containing one or more variables. To solve a variable equation, identify the values of the variables that cause the equality to hold true. The answer is known as the values of the variables that must satisfy the equality.
Equations can be categorized as identities or conditional equations.
w = (455.95-155.95)/(37.50)
=300/37.50
=8
So, number of weeks = 8
As a result, w = 8 and 37.5w + 155.95 = 455.95 is the solution.
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There are 3 feet in 1 yard, how many yards in 42 feet?
A.24 yards
B.32 yards
C.14 yards
D.12 yards
Answer:
c
Step-by-step explanation:
there are 14 yard in 42 feet
The graph shows the distribution of the amount of chicken (in ounces) that adults eat in one sitting.
A graph titled Chicken Consumption has amount (ounces) on the x-axis, going from 3.2 to 12.8 in increments of 1.2. The highest point of the curve is at 8.
Which statement describes the distribution?
The distribution is approximately Normal, with a mean of 8 ounces and a standard deviation of –1.2 ounces.
The distribution is approximately Normal, with a mean of 8 ounces and a standard deviation of 1.2 ounces.
The distribution is approximately Normal, with a mean of 1.2 ounces and a standard deviation of 8 ounces.
The distribution is uniform, with a mean of 8 ounces and a standard deviation of 1.2 ounces.
Using concepts of the normal and of the uniform distribution, it is found that the correct option is:
The distribution is approximately Normal, with a mean of 8 ounces and a standard deviation of 1.2 ounces.
In an uniform distribution, all outcomes are equally as likely, thus they have the same height.In the normal distribution, the outcomes with the highest likelihood are those closest to the mean, thus they have the highest height. This means that the mean of this distribution is 8.The standard deviation cannot be a negative value, so in this problem, it is 1.2, which means that the correct option is:The distribution is approximately Normal, with a mean of 8 ounces and a standard deviation of 1.2 ounces.
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Alan and Alan Connor have ₹6.70 in total
Alan has ₹1.70 more than Conner
Let a be the amount of money Alan has.
Let a be the amount of money Connor has
Set up a pair of simultaneous equations and solve to find out how much each person has
Answer: We can set up the following pair of simultaneous equations:
a + c = 6.70 (equation 1) (the total amount of money they have is ₹6.70)
a = c + 1.70 (equation 2) (Alan has ₹1.70 more than Conner)
We can substitute equation 2 into equation 1 to eliminate a:
(c + 1.70) + c = 6.70
Simplifying and solving for c:
2c + 1.70 = 6.70
2c = 5.00
c = 2.50
So Connor has ₹2.50.
We can substitute this value into equation 2 to find the value of a:
a = c + 1.70
a = 2.50 + 1.70
a = 4.20
Therefore, Alan has ₹4.20.
A pendulum swings in a arc at a slower rate of speed. The distance can be written as a sequence 5,2.5, 1.25,… Answer each of the following questions.
Step 1
Use a calculator to find the first term that equals 0 to the nearest hundredth-thousand
The first term that equals zero to the nearest hundred thousandth is; n= 21
\(The\text{ 21st term \lparen a}_{21})=0.000004768\)Step 2
The pendulum will not stop mathematically because the nth term is given as;
\(a_n=5(\frac{1}{2})^{n-1}\)Can approach zero but will never be zero
Step 3
At 10 swings the total distance traveled will be;
\(\begin{gathered} S_n=a_1\frac{1-r^n}{1-r} \\ =5\cdot \frac{1-0.5^{10}}{1-0.5} \\ =9.990234375 \end{gathered}\)At 50 swings the total distance traveled will be;
\(\begin{gathered} S_n=a_1\frac{1-r^n}{1-r} \\ =5\cdot\frac{1-0.5^{50}}{1-0.5} \\ =10 \end{gathered}\)Step 4
My observation and conclusion are that the Pendulum swings at distances that follow a geometric progression and the total distance traveled will be about 10.
(a) n= (Round up to the nearest integer.)A researcher wishes to estimate the proportion of adults who have high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.03 with 99% confidence if (a) she uses a previous estimate of 0.52? (b) she does not use any prior estimates? (A)n=
The required sample sizes are given as follows:
a) Previous estimate of 0.52: n = 1839.
b) No previous estimate: n = 1842.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)
In which the variables used to calculated these bounds are listed as follows:
\(\pi\) is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of 0.995, so the critical value is z = 2.575.
The margin of error is given as follows:
\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)
For an estimate of 0.52, the parameters are given as follows:
\(M = 0.03, \pi = 0.52\)
Hence the sample size is obtained as follows:
\(0.03 = 2.575\sqrt{\frac{0.52(0.48)}{n}}\)
\(0.03\sqrt{n} = 2.575\sqrt{0.52 \times 0.48}\)
\(\sqrt{n} = \frac{2.575\sqrt{0.52 \times 0.48}}{0.03}\)
\((\sqrt{n})^2 = \left(\frac{2.575\sqrt{0.52 \times 0.48}}{0.03}\right)^2\)
n = 1839.
Without a previous estimate, the sample size is given as follows:
\(0.03 = 2.575\sqrt{\frac{0.5(0.4)}{n}}\)
\(0.03\sqrt{n} = 2.575\sqrt{0.5 \times 0.5}\)
\(\sqrt{n} = \frac{2.575\sqrt{0.5 \times 0.5}}{0.03}\)
\((\sqrt{n})^2 = \left(\frac{2.575\sqrt{0.52 \times 0.5}}{0.03}\right)^2\)
n = 1842.
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the answer is actually 81
Answer:
okay i'll keep this in mind
Step-by-step explanation:
HELP! Can someone please help with the picture question below?
The probability that either event A or B will occur is 11/17.
We have,
The Addition Rule for Probability:
P(A U B) = P(A) + P(B) - P(A ∩ B),
where P(A U B) represents the probability of the union of events A and B, P(A) represents the probability of event A, P(B) represents the probability of event B, and P(A ∩ B) represents the probability of the intersection of events A and B.
Now,
P(A) = 9/17
P(B) = 2/17
There is no intersection of Q and B so,
P(A ∩ B) = 0
Now,
P(A U B) = P(A) + P(B) - P(A ∩ B),
Substituting the values.
P(A U B) = The probability that either event A or B will occur.
So,
P(A U B)
= 9/17 + 2/17 - 0
= 11/17
Thus,
The probability that either event A or B will occur is 11/17.
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Please help and show how you found the answer step by step.
According to the information, the perimeter of the triangle is ≈ 31.18
How to calculate the perimeter of the triangle?To find the distance between two points, we can use the distance formula:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's label the coordinates as follows:
Point 1: (-2, 3)
Point 2: (3, -2)
Now we can substitute these values into the distance formula:
distance = sqrt((3 - (-2))^2 + (-2 - 3)^2)
distance = sqrt((5)^2 + (-5)^2)
distance = sqrt(25 + 25)
distance = sqrt(50)
distance ≈ 7.07
Therefore, the distance from (-2, 3) to (3, -2) is approximately 7.07 units.
To find the perimeter of the triangle, we need to find the length of all three sides of the triangle and then add them up.
Using the distance formula, we can find the length of the sides:
Side 1: (-2,3) to (3,-2)
d = √[(3 - (-2))^2 + (-2 - 3)^2]
= √[5^2 + (-5)^2]
= √50
= 5√2
Side 2: (3,-2) to (-7,-2)
d = √[(-7 - 3)^2 + (-2 - (-2))^2]
= √[(-10)^2 + 0^2]
= 10
Side 3: (-7,-2) to (-2,3)
d = √[(-2 - (-7))^2 + (3 - (-2))^2]
= √[5^2 + 5^2]
= 5√2
Therefore, the perimeter of the triangle is:
5√2 + 10 + 5√2 = 15√2 + 10 ≈ 31.18 (rounded to two decimal places)
An two of the three sides are equal, so it is an isosceles triangle.
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.........................................
Answer:
Whats wrong??
Step-by-step explanation:
Answer:
you ok ?
Step-by-step explanation:
I dont know what the ......... means
In 2013, the population increases again by 15%. Write an expression that represents the deer population in 2013.
The expression that represents the deer population in 2013 is 1.15x.
What is an expression?Expression in mathematics is the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The Numbers constants, variables, operations, functions, brackets, punctuation, can all be represented by mathematical symbol that can be used to indicate the logical order of operations and other features.
We are Given that in 2013, the population increases again by 15%.
Now,
Let, the population in 2013 be x.
15% of x
=(x/100)*(15/100)
=0.15x
Here, x+0.15x
=1.15x
Therefore, the expression will be 1.15x.
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let be the amount of coffee (in ounces) that an undergraduate student at uiuc drinks per day. suppose we know that has a mean of 10 oz and a standard deviation of 5.2 oz. suppose there are 120 students in stat 107. assuming stat 107 students are a random sample, calculate the standard error of the average amount of coffee a stat 107 student drinks per day . is greater than 12.7 oz.
0.137606 the standard error of the average amount of coffee a stat 107 student drinks per day is greater than 12.7 oz.
What is standard deviation?Data dispersion in regard to the mean is quantified by a standard deviation, or "σ". Statisticians can assess if the data fits into a normal distribution or another mathematical connection using the standard deviation. The average, or mean, data point will be within one standard deviation of 68% of the data points if the data follow a normal curve.
Given that,
Standard deviation (σ) = 5.2 oz
mean (μ) = 10 oz
Number of students (n) = 120
As we know,
P ( z > 12.7 oz.) = P (z > [{x(avg.) - μ\(\sqrt{n}\)}/σ])
= P (z > [{12.7 - 10\(\sqrt{120}\)}/5.2])
= P (z > 1.86)
= 1 - P ( z < 1.86)
= 1 - 0.862394
= 0.137606
Thus, P( z > 12.7 oz.) = 0.137606
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Given f(x) = -2x^2 + 4, determine the slope of the secant line over the interval [-1, 2].
Answer: -2
Step-by-step explanation:
We know that the slope of a secant line over a interval [a,b] is given by :-
\(m=\dfrac{f(b)-f(a)}{b-a}\)
Given f(x) =\(-2x^2 + 4\)
Then, the slope of the secant line over the interval [-1, 2] is given by :-
\(m=\dfrac{f(2)-f(-1)}{2-(-1)}\\\\=\dfrac{(-2(2)^2+4)-(-2(-1)^2+4)}{2+1}\\\\=\dfrac{(-2(4)+4)-(-2(1)+4)}{3}\\\\=\dfrac{(-8+4)-(-2+4)}{3}\\\\=\dfrac{-4-2}{3}\\\\=\dfrac{-6}{3}\\\\=-1\)
Hence, the slope of the secant line over the interval [-1, 2] is -2.
In a group of 1,100 youths, each uses smart phones, either I-phone or Samsung or both or neither, 150 of them use only I-phone, 770 of them use Samsung and 900 use only one of these two smart phones. (1) Find the number of youths who use both of these smart phones. (ii) Find the number of youths who use neither of these smart phones.
The requried, 20 youths use both iPhone and Samsung, and 200 youths use neither iPhone nor Samsung.
Let A be the set of youths using only iPhones, B be the set of youths using only Samsung, and C be the set of youths using both. Then, we have:
|A| = 150
|B| = 770
|A ∪ B| = 900
We want to find |C| and |A ∩ B| (which is the number of youths using both).
Using the inclusion-exclusion principle, we have:
|A ∪ B| = |A| + |B| - |A ∩ B|
900 = 150 + 770 - |A ∩ B|
|A ∩ B| = 20
So, 20 youths use both iPhone and Samsung.
To find the number of youths who use neither, we can use the fact that:
|A ∪ B ∪ C| = 1100
|A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|
Plugging in the values we know, we get:
1100 = 150 + 770 + |C| - 20 - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|
|C| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C| = 200
Since the number of youths using both is 20, we have:
|A ∩ C| = |B ∩ C| = |A ∩ B ∩ C| = 0
So, we can simplify the equation to:
|C| = 200
Therefore, 200 youths use neither iPhone nor Samsung.
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On a piece of paper, graph fx) = 2• (0.5)*. Then determine which answer choice matches the graph you drew.
Answer:
Graph A
Step-by-step explanation:
The common ratio is less than 1, so the graph will be decreasing. The initial value is 2, so the y-intercept will be 2. Graph A fits this criteria.
I hope this helps :))
The graph A is correct.
What is a graph?A diagram (such as a series of one or more points, lines, line segments, curves, or areas) that represents the variation of a variable in comparison with that of one or more other variables.
The equation is,
\(y=2(0.5)^{x}\)
Plotting the graph, we get,
Option A
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solve and graph the inequality 4x > 16
Answer:
B.
Step-by-step explanation:
Answer: B
Step-by-step explanation:
Plz help me I’m md lost rn!
Answer:
6.4 km
Step-by-step explanation:
4x1.6
Answer:
6.4 km
Step-by-step explanation:
1.6 * 4 = 6.4
- The weight of 72 identical marbles is 183.6 grams. What is the weight of each marble? Explain how you
know the decimal point of your quotient is placed reasonably.
Answer:
the weight of each marble is 2.55 grams
Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis.
x = 2 + (y − 3)^2, x = 3
Step-by-step explanation:
I would be fighting if you answer the answer is that it's me but if you get it wrong it's not on me
how do i find these
The value of
1. v = 40cm
2. w= 126°
3. x = 30°
4. y = 63cm
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary.
The ratio of corresponding sides of similar triangles are equal.
Therefore ;
60/v = 72/48
48 × 60 = 72v
2880 = 72v
divide both sides by 72
v = 2880/72
v = 40cm
since the two triangles are similar w = 126°
x = 180-(126+24)
x = 180- 150
x = 30°
then;
y/42 = 72/48
48y = 42 × 72
48y = 3024
y = 3024/48
y = 63 cm
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What is an equation of the line that passes through the point (1,6) and is perpendicular to the line x+3y=27
DE bisects AC at point B. AC=a+23
and AB = 3a + 4. Find BC.
Y
X
13
2
X
(X) XS
X₁
IV
skill code: 1604005
TT
The length BC of the bisected line segment is: 11.5
What is the length of the line after bisection?Usually a line that bisects a segment usually divides that segment into two equal parts.
Now, we are told that DE bisects Line AC at point B where AB = 3a + 4.
Thus, from the idea of a bisected segment, we can easily say that:
2(3a + 4) = a + 23
6a + 8 = a + 23
6a - a = 23 - 8
6a = 15
a = 15/6
a = 5/2
a = 2.5
Thus:
AB = BC = 3(2.5) + 4
BC = 11.5
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Do this for me
pls im deprate
Answer:
216 \(cm^{2}\)
Step-by-step explanation:
The total area = the area of a square + the area of a circle
The area of the square = 11 x 11 = 121 \(cm^{2}\)
The area of the circle = \(\pi\)x\(\frac{11}{2}\)x\(\frac{11}{2}\) ≈ 95 \(cm^{2}\)
Therefore, the total area = 121 + 95 = 216 \(cm^{2}\)
Points A and B are on opposite sides of a lake. Another point, C. is 94.4 meters from Angle A. The measure of Angle A is 72° and the measure of Angle C is 30°. Find the distance between A and B.
To find the distance between points A and B, we can use trigonometry and the given information.
Let's label the distance between A and B as "d". We know that point C is 94.4 meters away from point A. From angle A, we have the measure of 72°, and from angle C, we have the measure of 30°.
Using trigonometry, we can use the tangent function to find the value of "d".
tan(72°) = d / 94.4
To solve for "d", we can rearrange the equation:
d = tan(72°) * 94.4
Using a calculator, we can evaluate the expression:
d ≈ 4.345 * 94.4
d ≈ 408.932
Therefore, the distance between points A and B is approximately 408.932 meters.
HELP WITH NUMBER ONE PLEASE!! (FACTORING)
Show me how you did it please!!!
Findthe
y -intercept
oftheparabolay = x2 + 3x − 6.
Answer:
(0, -6) is the y-intercept.