Using the Pythagorean Theorem, the length of the base is: 15 units.
What is the Pythagorean Theorem?The Pythagorean theorem is used to find any of the length of the legs or hypotenuse of a right triangle if we know any two measures of its side. The theorem is given as: the square of the hypotenuse = sum of the squares of the legs of the right triangle.
It can be expressed as c² = a² + b², where c is the longest side of the right triangle.
Note: The hypotenuse is the longest side of the triangle.
Thus, given the triangle in the image below, where:
c = 25
a = 20
b = length of the base
The expression that would be appropriate for this situation would be written based on the Pythagorean Theorem, which is:
b = √(c² - a²)
Substitute
b = √(25² - 20²)
b = 15 units
The length of the base is: 15 units.
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A circular pond has a diameter of 30 feet. The City of Puebla wants to build a fence enclosing the pond. How many feet of fencing does the city need to enclose the pond?
The amount of fencing feet the city needs to enclose the pond is 94.29 feet.
What is perimeter?Perimeter can be defined the total distance around an object.
To calculate the amount of fencing the city needs to enclose the pond, we use the formula for the perimeter of a circle.
Formula:
P = πd............ Equation 1Where:
P = Perimeter of the pondd = Diameter of the pondπ = PieFrom the question,
Given:
d = 30 feetπ = 22/7Substitute these values into equation 1
P = 30×22/7P = 94.29 feet.Hence, the feet of fencing needed is 94.29 feet.
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a 28-year-old man pays 118 for a one -year life insurance policy with coverage of 140,000 . if the probability that he will live through the year is 0.9993 , what is the expected value for the insurance policy?
The Insurance policy's anticipated value in this case is -20.
What is Insurance?
Insurance is a tool for risk management. You purchase protection against unforeseen financial losses when you purchase insurance. If something unpleasant happens to you, the insurance company pays you or someone else of your choosing.
Given,
Man pays -118 for one year
coverage = 140000
probability = 0.9993
The method used to calculate the insurance policy's expected value is:
= Chance that he won't live to see the end of the year * Coverage value - The cost of the insurance
= (1 - 0.9993)*140,000 - 118
= -20.
In this situation, the man's insurance coverage is expected to be worth -20.
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the manufacturer of cans of salmon that are supposed to have a net weight of 6 ounces tells you that the net weight is actually a normal random variable with a mean of 6.16 ounces and a standard deviation of 0.13 ounce. suppose that you draw a random sample of 38 cans. find the probability that the mean weight of the sample is less than 6.15 ounces.
The probability that the mean weight of the sample is less than 6.15 ounces as per the given data is 0.1806.
Mean, μ = 6.16 ounces
Standard Deviation, σ = 0.13 ounce
Sample size, n = 38
We are informed that the weight of the cans is distributed in a bell-shaped manner, which is a normal distribution.
Formula:
Z-score = ( x - ц) /standard deviation
Standard error due to sampling
=SD/√n
=0.13/ √(38)
=0.021
P(weight of the sample is less than 6.15 ounces)
P(X < 6.15) =P( Z< (6.15 - 6.16)/0.021 )
= P(Z> -0.476)
=0.1806 ( as per the Z- score table)
The probability that the sample's mean weight is less than 6.15 ounces is 0.1806.
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If a line on the coordinate plane increases as you read it from left to right, what do you know about the slope of that line??
The slope has a value of 1.
The slope has a value of 0.
The slope is positive.
The slope is negative.
The slope m of a line passing through two points (x1 , y1) and (x2 , y2) is:
m = (y2 − y1) / (x2 − x1)
If the graph of a line rises from left to right, the slope is positive.
What is slope ?
Slope is a ratio and can have a value that is positive, negative, equal to zero, or undefined. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run".
What is positive slope ?
A positive slope means that two variables are positively related—that is, when x increases, so does y, and when x decreases, y also decreases. Graphically, a positive slope means that as a line on the line graph moves from left to right, the line rises. We will learn in other sections that “price” and “quantity supplied” have a positive relationship; that is, firms will supply more when the price is higher.
The slope m of a line passing through two points (x1 , y1) and (x2 , y2) is:
m = (y2 − y1) / (x2 − x1)
If the graph of a line rises from left to right, the slope is positive.
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A trapezoid has an area of 35 mm2. What is the height of the trapezoid?
The height of the trapezoid is 5mm.
What is a trapezoid?
A trapezoid is a quadrilateral in American and Canadian English that has at least one pair of parallel sides. It is referred to as a trapezium in British and other varieties of English.
In Euclidean geometry, a trapezoid is invariably a convex quadrilateral. The trapezoid's parallel sides are referred to as its bases. If the remaining two sides are parallel, the trapezoid is a parallelogram and has two pairs of bases; if not, they are referred to as the legs (or lateral sides). A scalene trapezoid is a trapezoid without equal-sized sides.
Given: Area of trapezoid = [tex]35mm^{2}[/tex]
We know, area of trapezoid = [tex]\frac{(a+b)}{2} .h[/tex]
⇒ [tex]\frac{(8+6)}{2} .h=35[/tex]
⇒ [tex]7h=35[/tex]
⇒ [tex]h=5mm[/tex]
Hence, the height of the trapezoid is 5mm.
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What happens when you have a double negative?
the issue of capital punishment is a hotly debated topic. do more republicans than democrats support capital punishment? a researcher randomly selects 100 republicans and 100 democrats and asks them if they support or do not support capital punishment. in this problem, we want to make inferences about:
In this problem, we want to make inferences about comparing proportions from dependent samples. So the option F is correct.
In the given question, the issue of capital punishment is a hotly debated topic.
Do more republicans than democrats support capital punishment?
A researcher randomly selects 100 republicans and 100 democrats and asks them if they support or do not support capital punishment.
In this problem, we want to make inferences about:
A. one mean
B. comparing means from dependent samples
C. comparing means from two independent samples
D. one proportion
E. comparing proportions from two independent samples
F. comparing proportions from dependent samples
As we know that,
A hypothesis test can assist in figuring out whether a variation in the estimated proportions actually reflects a variation in the population proportions. An approximation of the normal distribution is shown by the difference between two proportions. The null hypothesis often argues that the two proportions are equal.
So, a researcher randomly selects 100 republicans and 100 democrats and asks them if they support or do not support capital punishment. In this problem, we want to make inferences about comparing proportions from dependent samples. So the option F is correct.
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How do you find (1+i)^4?
Using the square formula, the value of (1+i)^4 is -4.
The square formula is the algebraic identity which is used to find the square or difference of the sum of two terms. The square of sum of the two terms and can be calculated by multiplying the binomial by itself. The general form of square formula to find the square of the sum of two terms is given by: (a + b)^2 = a^2 + 2ab + b^2 where a and b are variables.
The given expression can be rewritten as binomial with exponent:
((1 + i)^2)^2
Using the square formula to find the square of the sum of two terms to the (1 + i)^2. Hence,
(1 + i)^2 = 1 + 2i + i^2
As 'i' iota is the square root of negative 1, i^2 = -1
1 + 2i -1 = 2i
Therefore,
(2i)^2 = 4i^2 = 4*-1 = -4
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4 Which trinomial is equivalent to
3(x-2)²-2(x-1)?
1) 3x²-2x-10
2)
3x² - 2x - 14
3)
3x² - 14x+10
4)
3x²-14x+14
Answer: 4) 3x²-14x+14
Explanation:
3(x-2)²-2(x-1)Use the binomial theorem (a−b)² = a² - 2ab + b² to expand (x-2)².
3(x²-4x+4)-2(x-1)Use the distributive property to multiply 3 by x²-4x+4.
3x²-12x+12-2(x-1)Use the distributive property to multiply −2 by x−1.
3x²-12x+12-2x+2Combine −12x and −2x to get −14x.
3x²−14x+12+2Add 12 and 2 to get 14.
3x²-14x+14It is 3x²+14x+14, the trinomial equivalent to 3(x-2)²-2(x-1). OPTION 4.
just these 2 questions
Answer:
nnnn
Step-by-step explanation:
hh
Find a polynomial function of degree 3 such that f(0)=17 and the square root of f(x) are 0,5 and 8
Answer:
f(x)=x^3 - 13x^2 + 40x + 17
Step-by-step explanation:
x-0=0 x-5=0 x-8=0
x=0 x=5 x=8
y=x(x-5)(x-8)+b ==> b is what's going to be used to find the equation so that
y=17 when x=0
17=0(0-5)(0-8)+b ==> plugin 0 for x and 17 for y
17=0*(-5)*(-8)+b ==> simplify
17=0+b ==> anything multiplied by 0 is 0.
b=17
Hence, the equation is:
y=x(x-5)(x-8)+17 ==> expand this equation
y=x*(x-5)(x-8) + 17
y=x*(x(x - 8) - 5(x - 8)) + 17 ==> distribute x-8 to x and -5
y=x*(x*x - 8x - 5x - (8)(-5)) + 17 ==> distribution property
y=x*(x^2 - 13x - (-40)) + 17 ==> simplify
y=x*(x^2 - 13x + 40) + 17 ==> subtracting a negative number is equivalent to
adding a positive number
y=x^3 - 13x^2 + 40x + 17 ==> multiply x with x^2, 13x, and 40 using the
distribution property.
Answer: f(x)=x^3 - 13x^2 + 40x + 17
Answer: Okay, lets explain.
Step-by-step explanation:Since 0, 5 & 8 are given as the zeros of the required 3rd degree polynomial f(x), therefore, one may take it as ; f(x) =k (x-0)(x-5)(x-8)
= k(x³−13x²+40) …. .. .(1) . Since f(10) = 17 (given), it implies 17 = k(1000 -1300 + 400) = 100 ==> k = 17/100 = 0.17 . Put this value of k in eq(1) and get the required polynomial.
every day jo practices her tennis serve by continually serving until she has had a total of 50 successful serves. if each of her serves is, independently of previous ones, successful with probability .4, approximately what is the probability that she will need more than 100 serves to accomplish her goal?
She needs 50 successful serves in the first 100 to attain her target. A 2% chance exists that this will occur.
She therefore has a 98% chance of requiring more than 100 serves to achieve her objective.
What is a probability?The study of probability, which is the potential of any event happening, is a field of mathematics that deals with the occurrence of random events. The probability value is given on a scale from 0 to 1.
How do you find probability?The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood that something will occur by the likelihood that it won't.
Jo must not complete 50 successful serves in her first 100 attempts in order to need more than 100 serves.
With n=100 and p=0.4, our probability sample of potential outcomes has a binomial distribution.
We will use a normal distribution to approximate n because it is a big enough number. The normal distribution's characteristics are as follows:
To ensure that she receives more than 100 serves, we must determine the likelihood that there will be fewer than 50 successful services. Such is:
We determine X's z value as follows:
Next, we have
That indicates that there is a 98% chance she will require more than 100 serves to accomplish her objective.
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can someone explain how to simplify fourth, fifth, and sixth roots
Step-by-step explanation:
how to simplfy the fifth root
the fifth root us a number that would multiply itself 5 times example √ 243 will be 3×3×3×3×3 =243 hope i helped u that the only one that i can explain beterwhat's the answer 7x + 7=7(x+_)
the answer is 1
Step-by-step explanation:
Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. Write the polynomial in standard form.
3,4+i
The conventional form of the polynomial is f(x)=x 28x+17. If polynomial function f has rational coefficients and a leading factor of 1, then it has the lowest degree.
How can you recognize a polynomial?A polynomial function is a function in an equation, such as the quadratic equation, cubic equation, etc., that only uses quasi integer powers or only positive integer coefficients of a variable. A polynomial with an exponent of 1 is, for instance, 2x+5.
As conjugate pairs make up complex zeros, we can infer that 4-i4-i is also a zero from the fact that 4+i4+i is also a zero.
A polynomial function's factor x-axa is one of the factors if aa is its zero. Consequently, the polynomial function is
f(x)=a[x-(4+i)] [x-(4-i)]
f(x)=a[x−(4+i)]
[x−(4−i)]
Expand:\sf(x)=a[x^2-(4-i)
x-(4+i)x+(4+i)(4-i)]
F(x) = a [x 2 (4i)x(4+i)x+(4+i)(4i)]
f(x)=a[x^2-4x+ix-4x-ix+
(16-i^2)]
F(x) = a [x 2 4x+ix4x+ix+(16i 2)]
f(x)=a[x^2-8x +(16-(-1))]
f(x)=a[x 2 −8x+(16−(−1))]
f(x)=a(x^2-8x +17)
f(x)=a(x 2 −8x+17)
Considering that a=1a=1 is the leading coefficient, this means:
color="#c34632" f(x)="x2-8x +17"
f(x)=x 2 −8x+17
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*URGENT* Sam has 2 part time jobs. At the grocery store, he earns $8/h and at the library, he earns $10/h. Before going on vacation, he would like to save $280. Determine the fewest number of hours he would need to work to reach his goal.
Unit rate is the quantity of an amount of something at a rate of one of another quantity.
The fewest number of hours he would need to work to reach his goal of $280 is 28 hours working in the library.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
Amount to earn = $280
Grocery store:
Earnings per hour = $8
1 hour = $8
Multiply 280/8 on both sides.
280/8 x 1 hour = $280
35 hours = $280
Library:
Earnings per hour = $10
1 hour = $10
Multiply 280/10 on both sides.
28 hours = $280
We see that,
Working in the Library would make $280 in fewer hours than working in the grocery store.
Thus,
The fewest number of hours he would need to work to reach his goal of $280 is 28 hours working in the library.
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Write an equation of the line passing through point p(3 8) that is parallel to the line y=1/5(x+4).
The equation of the line is y = 1/5(x + 37). The standard equation of a instantly line is y = mx + c, in which m is the gradient, and y = c is the cost in which the road cuts the y-axis.
This range c is known as the intercept at the y-axis. The equation of a instantly line with gradient m and intercept c at the y-axis is y = mx + c. The equation of a instantly line is y=mx+c y = m x + c m is the gradient and c is the peak at which the road crosses the y -axis, additionally referred to as the y -intercept.
Since equation have new line which is parallel y = 1/5(x + 4), and 1/5 is most the gradient for the line y = 1/5(x + 4), this is the new line is 1/5.
Using the equation we can form a line in slope-point form,
[tex]\frac{y-y_{1} }{x-x_{1} } = m[/tex]
where (x₁, y₁) = (3, 8) and m = 1/5
Substituting the values for all variables into the equation, we have
[tex]\frac{y-y_{1} }{x-x_{1} } = m\\\frac{y-8 }{x-3 } = m\\[/tex]
Cross-multiplying. we have
5(y - 8) = x - 3
Expanding the bracket, we have
5y - 40 = x - 3
5y = x - 3 + 40
5y = x + 37
y = 1/5(x + 37)
So, the equation of the line is y = 1/5(x + 37)
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Can someone help me with this problem.
The value of x in the first question is 11 and the value of y is 3.
The value of x in the second question is 4 and the value of y is 4.
The value of x in the third question is -5 23/26 and the value of y is -1/13
What are the solutions of the equations?2x + y = 25 equation 1
2x - 3y = 13 equation 2
The first step is to subtract equation 2 from equation 1:
-4y = -12
Divide both sides of the equation by -4
y = -12 / -4
y = 3
Substitute for y in equation 1:
2x + 3 = 25
2x = 25 - 3
2x = 22
x = 22 / 2
x = 11
-3x + 4y = -18 equation 1
x = -2y - 4
x + 2y = -4 equation 2
Multiply equation 2 by 2
2x + 4y = -8 equation 3
Subtract equation 3 from equation 2:
-5x = -20
Divide both sides of the equation by -5
x = -20 / -5
x = 4
Substitute for x in equation 2:
4 + 2y = -4
4 + 4 = 2y
8 = 2y
y = 8/2
y = 4
-2x + 3y = -15 equation 1
3x + 2y = -23 equation 2
Multiply equation 1 by 3 and equation 2 by 2
-6x + 9y = -45 equation 3
6x + 4y = -46 equation 4
Add equation 3 and equation4 together
13y = -1
y = -1/13
Substitute for y in equation 1:
-2x + 3(-1/13) = -15
-2x -3/13 = -15
-2x = -15 + 3/13
-2x = 11 10/13
x = 11 10/13 ÷ -2
x = 153/13 x -1/2
x = -153/26
x =-5 23/26
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how many length m words can be formed from an n-letter alphabet, if no letter is used more than once? (b) how many length m words can be formed from an n-letter alphabet, if letters can be reused? (c) how many binary relations are there from set a to set b when jaj d m and jbj d n? (d) how many total injective functions are there from set a to set b, where jaj d m and jbj d n m
As per the combination method, there are 120, 5 length m words can be formed from an n-letter alphabet, if no letter is used more than once.
Combination method:
in statistics, mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter is known as combination method.
Given,
Here we need to find how many length m words can be formed from an n-letter alphabet, if no letter is used more than once.
Let us consider letters (a,b,c,d,e) how many distinct n length words can be formed.
Here we note that every word can contain same letter m times at most.
So, it can be calculated as,
=> 5 x 4 x 3 x 2 x 1
=> 120
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translate the description as an algebraic expression: half the difference of 2 and b
suppose that from previous evidence, anthropologists had believed that for each 1 mm increase in chord length, cranial capacity would be expected to increase by 20 cm3. do the data given here strongly contradict prior belief? use a 0.05 level of significance.
The data does contradict with the prior evidence
To determine whether the data presented here are significantly inconsistent with previous assumptions, a statistical test was performed to verify that the observed relationship between tendon length and cranial volume was significantly greater than the expected relationship. You have to decide if they are different.
To do this, fit a line to the data using linear regression analysis and test the hypothesis that the slope of the line is equal to 20 cm3/mm. If the p-value for this hypothesis test is less than 0.05, you can conclude that the data are inconsistent with previous assumptions at the 0.05 significance level.
It is crucial to realize that this analysis assumes that the relationship between tendon length and cranial volume is linear.
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Males and females are observed to react differently to a given set of circumstances. It has been observed that 70% of the females react positively to these circumstances, whereas only 40% of males react positively. A group of 20 people, 15 female and 5 male, was subjected to these circumstances, and the subjects were asked to describe their reactions on a written questionnaire. A response picked at random from the 20 was negative. What is the probability that it was that of a male?
The probability that it was that of a male is 2/5 .
This problem of probability can be solved using Baye's Theorem . In simple terms , Bayes' Theorem states that the conditional probability of an event, based on the occurrence of another event, is equal to the likelihood of the second event given the first event multiplied by the probability of the first event. Hence , proceeding accordingly -
Given in the question is :
P(Males reacting negatively = M) = 1-40%= 60% = 60/100
P(Females reacting negatively = F) = 1-70%= 30% = 30/100
Now , P(Females' response being selected= f) = 15/20
P(Males' response being selected = m ) = 5/20
P(M/m) = P(M) P(m)/ P(M) P(m) + P(F) P(f)
⇒ 5/30 × 60/100 ÷ 5/30 × 60/100 + 15/20 × 30/100
⇒ 300/300+450
⇒ 300/750
⇒ 2/5
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How do you simplify (2−i) / (5+i) ?
To simplify [tex]\frac{2-i}{5+i} = \frac{9}{26} -\frac{7}{26} i[/tex] , multiply the numerator and denominator by the conjugate of the denominator.
A complex number's conjugate A+bi equals a-bi. A real number is the result of a complex number and its conjugate. That fact will be used here.
[tex]\frac{2-i}{5+i} =\frac{2-i}{5+i} . \frac{5-i}{5-i}[/tex]
[tex]= \frac{(2-i)(5-i)}{(5+i)(5-i)}[/tex]
[tex]=\frac{10-2i-5i-1}{25-5i+5i+1}[/tex]
[tex]=\frac{9-7i}{26}[/tex]
[tex]=\frac{9}{26}-\frac{7}{26}i[/tex]
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The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x=1 and x=0, and a root of multiplicity 1 at x=−5
Find a possible formula for P(x).
P(x)=
The possible formula for polynomial is P(x)=x⁵+3x⁴-9x³+5x²
What is Polynomial?Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.
Given,
The polynomial of degree 5.
P(x) has leading coefficient 1, has roots of multiplicity 2 at x=1 and x=0, and a root of multiplicity 1 at x=−5
Each root corresponds to a linear factor, so we can write
P(x)=x²(x-1)²(x+5)
=x²(x²+1-2x)(x+5)
=(x⁴+x²-2x³)(x+5)
=x⁵+x³-2x⁴+5x⁴+5x²-10x³
=x⁵+3x⁴-9x³+5x²
Hence, the possible formula for polynomial is P(x)=x⁵+3x⁴-9x³+5x²
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How do you define a variable and write an algebraic expression for the phrase: 12 less than a number?
The expression is x-12.
12 less than a number means subtracting 12 from that number.
So, 12 less than 20 is 8, because is 20−12, 12 less than 12 is 0, because it's 12−12, and so on.
But since the number you need to subtract from is unknown, it's a variable, and you can call it as you like, suppose x. So, using the variable we can write an expression that holds for any number, which always means "take 12 away from my number". If your number is x, the expression would be x-12
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There are 3 fewer yellow beads than red beads. There are twice as many green beads as yellow beads. Write expressions for the number of red, green, and yellow beads.
Answer:
yellow = red - 3 and green = yellow x 2 and red = yellow + 3
or
green= (red-3) x 2
Step-by-step explanation:
Three fewer yellow than read is the same as saying red -3
twice as many green as yellow is the same as yellow x 2
if green is yellow x 2 you can substitute yellow for the equation to find yellow
you can flip the equation for yellow around by doing inverse operations. To have the equation equal red you need to move the three by doing its inverse. The opposite of subtraction is addition so you'd add 3 to each side, getting rid of the -3 and isolating the red to make the equation red=yellow+3
f(x) = x² + 6x-4
g(x) = 2x - 8
Find: (fog)(x)
fog(x) =4x²+44x+12,
f(x) is quadratic function whose value is x²+6x -4 at x.
so , we have asked the value of f(x) at x=g(x) , which another function whose value is 2x-8 .
so, by the concept of composition of functions we have to put the value 2x-8 in place of x in the f(x) function to get fog(x).
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The table below shows the amount of money needed to buy certain amounts of fabric. If the price is the same for each yard, how much money would 12 yards of fabric cost?
Correct answer will get brainliest
The equation is y = (5/3)x. Then the cost of the 12 yards of fabric will be $20. Then the correct option is B.
What is the equation of a line passing through two points?Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).
Then the equation of the line is given as,
[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]
The two points are (3, 5) and (6, 10).
Let 'x' be the number of yards of fabric and 'y' be the cost in dollars. Then the equation is given as,
(y - 5) = [(10 - 5) / (6 - 3)](x - 3)
y - 5= (5/3)x - 5
y = (5/3)x
The cost of the 12 yards of fabric is given as,
y = (5/3) × 12
y = 5 × 4
y = $20
The equation is y = (5/3)x. Then the cost of the 12 yards of fabric will be $20. Then the correct option is B.
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Solve the given proportion 7/x 21/6 x = [?] Enter
Answer:
x=2
Step-by-step explanation:
7÷x=22÷6
cross multiply
7×6=21×x
21x=42
21x/21=42/21
x=2
10 yards is how many inches?
Answer:
360 inches.
Step-by-step explanation:
because 1 yard is 36 inches (3 rulers) so just multiply 36 by your number of yards.
