Please help!
Matrix Pre-calc

Answer:

60

Step-by-step explanation:

50+70=120

180-20=60

Answer:

120°

Step-by-step explanation:

Your question didn't include an image or angle names, so it was pretty confusing to get what you were asking for. If you were asking for the exterior angle of the missing angle, then here's your answer:

The 3 angle measures of a triangle will always equal 180.

Since we've already got two angles, all we need to do is a simple equation to get our missing angle:

180-(50+70)=60

Now that we've got the missing angle, we need to calculate the exterior angle, the thing we're here for. We know (hopefully at this point) that an exterior angle and its interior angle are a linear pair, meaning that the two add up to 180. Knowing this, we can do this equation to finish off the question:

180-60=120

And there's your answer, 120°

There's also a shorter way of doing this, let me know if you'd like to see it. But for now, hope I helped!

The probabilities are given as follows:

The probabilities are called identifying the desired outcomes from the distribution of the number of children per parent.

Hence the probability of fewer than 4 siblings is of:

P(X < 4) = P(X = 1) + P(X = 2) + P(X = 3) = 0.266 + 0.322 + 0.149 = 0.737.

The probability of at least 5 siblings is of:

P(X >= 5) = P(X = 5) + P(X = 6) + P(X > 6) = 0.059 + 0.032 + 0.02 = 0.111.

The probability that the student is not an only child is given as follows:

P(X > 1) = 1 - P(X = 1) = 1 - 0.266 = 0.734.

The distribution is given as follows:

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Answer: x-18

Step-by-step explanation:

Answer:

Solution = (5, 2)

Step-by-step explanation:

Step 1: Solve for y in 9x + 2y = 49

    1. 9x + 2y = 49 → 2y = -9x + 49 → y = -4.5x + 24.5

Step 2: Substitute -4.5x + 24.5 for y in -3x + 5y = -5

    2. -3x + 5(-4.5x + 24.5) = -5

Step 3: Solve for x

    3. -3x - 22.5x + 122.5 = -5 → -25.5x + 122.5 = -5 → -25.5x = -127.5 → x = 5

Step 4: Substitute 5 for x in -3x + 5y = -5

    4. -3(5) + 5y = -5 → -15 + 5y = -5 → 5y = 10 → y = 2

Hope this helps :)

A) The data models a geometric sequence

B) Using a recursive formula, the time she will complete station 5 is; 2

C) Using a explicit formula, the time she will complete station 9 is; 512

A)  From the given coordinates (1, 3), (2, 6), (3, 12), (4, 24), we can say that when x increases by 1, y is multiplied by 2. Thus, as the quotient between consecutive terms is the same, the data depicts a geometric sequence.

B) The recursive formula for a geometric sequence with common ratio r and first term a₁ is given by the formula:

f(n) = a₁(r)ⁿ⁻¹

Since a₁ = 2 and r = 1, then we have;

f(1) = 2(1)¹⁻¹

f(1) = 2

f(5) = 2

C) The explicit formula from the calculations above will be;

aₙ = 2ⁿ

Thus;

a₉ = 2⁹

a₉ = 512

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Answer: 5[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

19=(x+(2x+2))
Subtract 2 from each side
17=x+2x
17=3x
Divide each side by 3
[tex]\frac{17}{3}[/tex] = x
5 [tex]\frac{2}{3}[/tex] = x

Answer:

Step-by-step explanation:

The total amount of infection needed to develop symptoms of measles is 7840

Consider the model,

N(t)= f(t)=-t(t-21)(t+1).

The area of the graph of N(t) from t=0 to t = 12 is,

N(t)dt

Use six subintervals and their midpoints to estimate the above as follows:

Here, a=0,b=12, n=6

The length of each subinterval is,

h= b-a/n = 12-0/6

=2

So, the midpoints of each subinterval are 1, 3, 5, 7, 9, and 11.

Use Midpoint Rule,

A = [N(t)dt]

= At[ƒ (1) + ƒ (3) + ƒ (5) +ƒ(7)+ƒ(9)+ƒ(11)] =2[40+216+480+784+1080+1320]

= 7840

Thus, the total amount of infection needed to develop symptoms of measles is 7840.

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a) The student's work is False and the strategy is incorrect as the fraction should be 1/16

b) The fraction 1/16  as decimal is 0.0625

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number be = A

Now the value of A is A = 6 1/4 %

The value of A = 6.25 %

Now , the value of 6.25 % = 6.25 / 100

The fractional form can be substituted by dividing the numerator and denominator by 25 , we get

A = 6.25 / 100

A = ( ( 6.25 ) / 25 ) / ( 100 / 25 )

A = ( 0.25 ) / 4

The value of A = 0.25 / 4

The value of A = 0.0625

And it can be represented in the fractional form as

A = 0.25 / 4

The value of 0.25 = 1/4

Substituting the value of 0.25 in the equation , we get

A = ( 1/4 ) / 4

A = 1/16

Therefore , the value of A = 1/16

b)

The decimal from of the number 1/16 is 0.0625

The mistake the student did was while dividing the number by 100 to convert the percentage , the student evaluated the number 625 instead of 6.25 , so after avoiding the error , we get the fraction as 1/16

The decimal from of the number 1/16 is 0.0625

Hence ,

a) The student's work is False and the strategy is incorrect as the fraction should be 1/16

b) The fraction 1/16  as decimal is 0.0625

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Answer:

3,31

Step-by-step explanation:

i dont got steps for this but i think thats the right answer

The equivalent expressions of each number are respectively;

1) 2(x - 2) = -7 + 6x - 4x + 3

2) (x + 14) - (8 - 2x) = 9x - 2(3x - 3)

3) 3(x + 5) = -2x + 9 + 5x + 6

4) -4(x + 1) + 5x =  (7 - 2x) + (3x - 11)

5) (7 + 5x) + (4x - 1) = -3x + 6 + 4x

The properties of algebra include associative property, distributive property, Identity property, Inverse property, e.t.c.

Now, let us simplify the terms on the right;

a) (7 - 2x) + (3x - 11)

Expanding the brackets gives us;

7 - 2x + 3x - 11

= x - 4

This can also be expressed as;

-4(x + 1) + 5x

b) -7 + 6x - 4x + 3

Simplifying gives;

2x - 4

= 2(x - 2)

c) 9x - 2(3x - 3)

Simplifying gives;

9x - 6x + 6

3x + 6

It can also be written as;

(x + 14) - (8 - 2x)

d) -3x + 6 + 4x

Simplifying gives;

x + 6

This can also be expressed as;

(7 + 5x) + (4x - 1)

e) -2x + 9 + 5x + 6

This can also be expressed as;

3x + 15

3(x + 5)

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Answer:

[tex]\boxed{4.} \quad (7-2x)+(3x-11)[/tex]

[tex]\boxed{1.} \quad -7+6x-4x+3[/tex]

[tex]\boxed{2.} \quad 9x-2(3x-3)[/tex]

[tex]\boxed{5.} \quad -3x+6+4x[/tex]

[tex]\boxed{3.} \quad -2x+9+5x+6[/tex]

Step-by-step explanation:

Simplify the given expressions numbered 1 through 5:

[tex]\begin{aligned}\textsf{1.} \quad 2(x-2)&=2 \cdot x + 2 \cdot (-2)\\&=2x-4\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{2.} \quad (x+14)-(8-2x)&=x+14-8+2x\\&=x+2x+14-8\\&=3x+6\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{3.} \quad 3(x+5)&=3 \cdot x + 3 \cdot 5\\&=3x+15\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{4.} \quad -4(x+1)+5x&=-4 \cdot x -4 \cdot 1+5x\\&=-4x-4+5x\\&=5x-4x-4\\&=x-4\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{5.} \quad (7+5x)+(-4x-1)&=7+5x-4x-1\\&=5x-4x+7-1\\&=x+6\end{aligned}[/tex]

Simplify the given answer expressions:

[tex]\begin{aligned}(7-2x)+(3x-11)&=7-2x+3x-11\\&=3x-2x+11-11\\&=x-4\end{aligned}[/tex]

[tex]\begin{aligned}-7+6x-4x+3&=6x-4x+3-7\\&=2x-4\end{aligned}[/tex]

[tex]\begin{aligned}9x-2(3x-3)&=9x-2 \cdot 3x-2 \cdot (-3)\\&=9x-6x+6\\&=3x+6\end{aligned}[/tex]

[tex]\begin{aligned}-3x+6+4x&=4x-3x+6\\&=x+6\end{aligned}[/tex]

[tex]\begin{aligned}-2x+9+5x+6&=5x-2x+9+6\\&=3x+15\end{aligned}[/tex]

Therefore, the matching pairs of equivalent expressions are:

[tex]\boxed{4.} \quad (7-2x)+(3x-11)[/tex]

[tex]\boxed{1.} \quad -7+6x-4x+3[/tex]

[tex]\boxed{2.} \quad 9x-2(3x-3)[/tex]

[tex]\boxed{5.} \quad -3x+6+4x[/tex]

[tex]\boxed{3.} \quad -2x+9+5x+6[/tex]

Answer:

6 sides

Step-by-step explanation:

since the measure of an interior angle of a polygon can be found with the formula 180(n-2) / n where n is the number of sides we can substitute 120 to the answer and cross multiply to find that

120n = 180(n-2)

120n = 180n-360

360 = 60n

n = 6

Answer:

Step-by-step explanation:

y=4x+2

For a point to be perpendicular to a line

then the product of the two gradients must be negative one (I.e, m1×m2=-1)

where m1= 4

m2=-(1/m1)

m2=-1/4

point (7,-6)

x1=7 y1=-6

from the general equation of a line

y-y1=m(x-x1)

y-(-6)=-1/4(x-7)

y+6=-1/4(x-7)

y+6=-1/4x+7/4

y+1/4x=(7/4)-6

y+1/4x=-17/4

y+1/4x+17/4=0

4y+x+17=0

Answer:

y=-3x+2 y=-x-4

Step-by-step explanation:

The largest number of the five positive integers is 146.

Mean:

The mean is the mathematical average of a set of two or more numbers. The arithmetic mean and the geometric mean are two types of mean that can be calculated. The formula for calculating the arithmetic mean is to add up the numbers in a set and divide by the total quantity of numbers in the set.

Median:

The median is the middle value in a set of data. First, organize and order the data from smallest to largest. To find the midpoint value, divide the number of observations by two. If there are an odd number of observations, round that number up, and the value in that position is the median.

Here we have to find the largest integer.

Data given:

Four of the five integers are 8, 18, 36, and 62.

It is given that mean of five numbers 1.5 times their median.

mean = (8+18+36+62 + x)/5

median = 36

mean = 1.5 × median

(124 + x) / 5 = 1.5 × 36

124 + x = 5 × 54

x = 270 - 124

  = 146

Therefore we get the largest number as 146.

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Answer: 40%

Step-by-step explanation: 18/45 = x/100

divide 100 by 45 and you get 2.22 repeating.

multiply 2.22 by 18 and you get 40%

Answer: x ∈ {-0.5, -5, -12.5}

Step-by-step explanation: To solve the inequality 2x³ + 21x² + 60x + 25 > 0, we first need to find the values of x that make the inequality true. We can do this by setting the expression equal to 0 and solving for x.

We can start by factoring the expression to make it easier to solve. Notice that 2x³ + 21x² + 60x + 25 is a polynomial with a leading coefficient of 2 and a constant term of 25. This means that it has the form (x + a)(x + b)(x + c), where a, b, and c are constants.

We can start by factoring out the common factor of 2x from the first two terms: 2x³ + 21x² + 60x + 25 = 2x(x² + 10.5x + 12.5). Now we can see that the expression has the form (x + a)(x + b)(x + c), where a = 0.5, b = 5, and c = 12.5.

So, we can rewrite the expression as (x + 0.5)(x + 5)(x + 12.5) = 0. Now we can solve for x by setting each factor equal to 0 and solving for x:

x + 0.5 = 0 => x = -0.5

x + 5 = 0 => x = -5

x + 12.5 = 0 => x = -12.5

Therefore, the values of x that make the inequality true are x = -0.5, x = -5, and x = -12.5.

Now we need to determine which of these values make the inequality 2x³ + 21x² + 60x + 25 > 0 true. To do this, we can substitute each of the values of x into the inequality and see which ones make the inequality true.

When x = -0.5, the inequality becomes 2(-0.5)³ + 21(-0.5)² + 60(-0.5) + 25 > 0, which simplifies to -0.5 + 5.25 - 15 + 25 > 0. This is true, because the left-hand side is 29 > 0.

When x = -5, the inequality becomes 2(-5)³ + 21(-5)² + 60(-5) + 25 > 0, which simplifies to -125 + 525 - 300 + 25 > 0. This is also true, because the left-hand side is 225 > 0.

When x = -12.5, the inequality becomes 2(-12.5)³ + 21(-12.5)² + 60(-12.5) + 25 > 0, which simplifies to -391.25 + 1181.25 - 750 + 25 > 0. This is also true, because the left-hand side is 1147.5 > 0.

Therefore, the solution to the inequality is x ∈ {-0.5, -5, -12.5}. This means that the values of x that make the inequality true are x = -0.5, x = -5, and x = -12.5. The inequality is satisfied when x is any of these values.

False. Because a 95% confidence interval is two standard errors on either side of the mean.

What is a 95% confidence interval?

If 100 separate samples were taken and a 95% confidence interval was calculated for each sample, then around 95 of the 100 confidence intervals would contain the actual mean value (), according to the definition of a 95% confidence interval.

For a 95% confidence interval, the value lies within 2 standard deviations of the normal distribution.

For upper and lower bounds one standard error on either side of the mean is 68%.

So, the 95% confidence interval is two standard errors on either side of the mean.

Hence, the given statement is False.

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The estimate value of the standard deviation of the population ( manufacturing process) is 0.125..

The standard deviations is estimated to be one fourth of the sample range (as most of data values are within two standard deviations of the mean).

We have given that,

A sample of manufacturing process.

Sample size, n = 5

Mean of sample ranges = 0.50

we have to calculate the estimate of standard deviations of population.

thus , we estimate the standard deviations as fourth of the mean of the sample ranges is

S = Mean of sample ranges/4

=> S = 0.50/4

=> S = 0.125

Hence, the standard deviation of the population is estimated as 0.125..

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the polynomial that represents the volume of the box is is 6x^3 +5x^2 -3x-2

V=lwh

l=x+1

w=2x+1

h=3x-2

V=(x+1)(2x+1)(3x-2)

V=(x*2x+x*1+1*2x+1*1)(3x-2)

V=(2x²+x+2x+1)(3x-2)

V=(2x²+3x+1)(3x-2)

V=2x²*3x+2x²*(-2)+3x*3x+3x*(-2)+1*3x+1*(-2)

V=6x³-4x²+9x²-6x+3x-2

V=6x³+5x²-3x-2

complete question is

Find the volume of the box. Use the formula V = lwh.

Rectangular box with sides x plus 1, 2x plus 1, and 3x minus 2.

6x3 – 2

6x3+ x – 2

6x3 – 13x2 – 3x – 2

6x3 + 5x2 – 3x – 2

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The slope of both functions remains the same, there is no effect of the value of k on a slope.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.

Change in the value of y-intercept. For f(x) y-intercept is 5 and for g(x) y-intercept is 2.

The given functions are :

f(x) = 2x + 5

g(x) = ( 2x + 5) -3

From the graph of both functions,

Let us consider two pairs of coordinates to find the slope,

For f(x)

(0,5) and ( -2, 1)

The slope of f(x)

m= ( 1- 5) / (-2 -0)

m= 2

For g(x) at (0,2) and (-1, 0) slope of g(x),

m = ( 0-2) / (-1-0)

m = 2

The slope remains unaffected.

y-intercept of f(x) , put x = 0

⇒ y = 5

y-intercept of g(x) , put x = 0

y =(0+ 5) -3

y = 2

Change in the value of y-intercept due to the value of k = -3.

Therefore, for the given function f(x) = 2x + 5 and g(x) = ( 2x + 5) -3, the effects of the value of k on slope and y-intercept are as follows:

The slope of both functions remains the same, there is no effect of the value of k on a slope.

Change in the value of y-intercept. For f(x) y-intercept is 5 and for g(x) y-intercept is 2.

The graph is attached.

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Answer: C

Step-by-step explanation:

-2 and 2 add up to 0

Answer:

c

Step-by-step explanation:

-2 + 2 =0

The solution to the system equation  is (x, y, z, w) = (23, 12, 3, 1).

What is equation?

An equation could be a formula that expresses the equality of 2 expressions, by connecting them with the sign =

Main body:

Here is a system of linear equations that represents the situation.

x +5y +10z +20w = 133 . . . total amount earned

x +y +z +w = 39 . . . . . . . . . total number of bills

y = 4z . . . . . . . . . . . . . . . . . . the number of 5s is 4 times the number of 10s

x = 2y -1 . . . . . . . . . . . . . . . . the number of 1s is 1 less than twice the number of 5s

_____

We can substitute for x and z in the first two equations:

... (2y-1) +5y +10(y/4) +20w = 133

... (2y-1) +y +(y/4) +w = 39

These simplify to

... 9.5y +20w = 134

... 3.25y +w = 40

Solving by your favorite method, you get

... y = 12

... w = 1

So the other values can be found to be

... x = 2·12 -1 = 23

... z = 12/4 = 3

hence ,The solution to the system is (x, y, z, w) = (23, 12, 3, 1).

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The probability that the couple will have more than 2 girls is 1/2.

Here, we are given that a couple is planning to have 3 children.

Let us list down all the possible combination of outcomes-

GGG, GGB, GBB, BBB

Here G stands for a girl and B for a boy.

Thus, there are a total of 4 outcomes. We need to find the probability that the number of girls is greater than or equal to 2.

Out of the listed outcomes, 2 combinations- GGG and GGB have number of girls ≥ 2.

We know that probability = Number of favorable outcomes/ total number of outcomes

P(x ≥ 2) = 2/4

= 1/2

Thus, the probability that the couple will have more than 2 girls is 1/2.

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The Wason selection test measures a person's ability to recognize information that challenges a certain hypothesis, in this case, a type of conditional hypothesis. if P, then Q.

Given,

Wason's Card;

A popular tool for studying problem resolution that was developed in 1966 by English psychologist Peter C(athcart) Wason (1924–2003). The uppermost faces of the four cards, which are arranged on a table, display the letters and numerals E, K, 4, and 7.

What is demonstrated by the Wason selection task?

As a result, the Wason selection test gauges how well people can spot evidence that refutes a certain hypothesis, in this case, a conditional hypothesis of the type. P, then Q if.

For example;-

The majority of people have no trouble choosing the proper cards ("16" and "drinking beer") if the rule is "If you are drinking alcohol, then you must be over 18" and the cards contain an age and beverage on one side, respectively.

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Both the pairs of opposite sides in a parallelogram are parallel and congruent.

According to the question,

We've proved that one pair of sides in parallelogram must be congruent

Let ABCD is a parallelogram ,

We know that AB // CD

Here, AC is transversal for the parallel lines AB and CD

So, ∠BAC = ∠DCA    (Using interior angle property) --------(1)

Similarly , We also know that BC // AD

=> ∠BCA = ∠DAC -----------(2)

Now , In ΔABC and ΔADC,

Therefore , ΔABC ≅ ΔADC    (as per ASA congruence rule)

Therefore , AB = CD and BC=AD   (Corresponding sides of congruent triangles are equal)

Hence , Both the pairs of opposite sides in a parallelogram are parallel and congruent.

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The equation of the circle centered at (−5, 8) and having a radius of 7 is (x + 5)² + (y - 8)² = 49.

The standard form of the equation of a circle is expressed as;

x² + y² = r²

The horizontal (h) and vertical (k) translations represents the center of the circle.

Hence;

(x - h)² + (y - k)² = r²

Given the data in the question;

Center of the circle: (−5, 8)

Now, plug the values of h, k and r into the equation above and simplify,

(x - h)² + (y - k)² = r²

( x - (-5) )² + ( y - 8 )² = 7²

(x + 5)² + (y - 8)² = 49

Therefore, the equation of the circle is (x + 5)² + (y - 8)² = 49.

Hence, option A is the correct answer.

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As per the concept of z - score, the percentile would this client's score is 0.4772

Z - score:

In statistics, z - score is also termed the standard score, is used to determine how much each data point position is away from its mean. Where as in other words, it measures the deviation of x (data point) in terms of the standard deviations. Here the percentage of the population above or below the score can be obtained using z tables.

Given,

A test has a mean of 100 and a standard deviation of 15. a client scores 130 on the test.

Here we need to find at what percentile (rounded off) would this client's score place her.

As per the formula of z score, here we have the values,

mean = 100

standard deviation = 15

Score = 130

Therefore, the z score is calculated as,

=> z score = (130 - 100) / 15

=> z score = 30 / 15

=> z score = 2

According to the z score table the resulting value is 0.4772.

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It will take 51.9 seconds to return to sea level.

The rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered.

Using the speed - distance relationship, the time taken for the scientist to travel back to sea level would be 51.9 seconds

Distance = Speed × time

First travel :

Distance covered = 90 × 3.5 = 315 feet

Second travel :

Distance covered = 30 × 2.2 = 66 feet

Net change in position from sea level :

(315 - 66) feet = 249 feet

Maximum speed = 4.8 feet per second

Time taken = Distance / speed

Time taken = 249 ÷ 4.8 = 51.875 seconds

Hence, it will take 51.9 seconds to return to sea level.

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