By rounding to 1 significant figure, estimate
40.73
×
1.06

a. Using the graph, the estimated solution is: (-2, -0.6).

b. Solving algebraically, the exact solution is: (-2, -4/6).

The solution 0f a system of equations is that point of intersection where the lines of the two equations meet when they are plotted on a graph.

a. Given the graph of the equations, 2x - 3y = -2 and x + 1.5y = -3, the estimated solution, which is the point of the intersection of both lines can be, (-2, -0.5)

b. To get the exact solution, we would solve algebraically as shown below:

2x - 3y = -2 --> eqn. 1

x + 1.5y = -3 --> eqn. 2

Rewrite eqn. 2:

x = -3 - 1.5y --> eqn. 3

Substitute the value of x into eqn. 1:

2(-3 - 1.5y) - 3y = -2

-6 - 3y - 3y = -2

-6 - 6y = -2

-6y = -2 + 6

-6y = 4

y = 4/-6

y = -4/6

Substitute the value of y into eqn. 3:

x = -3 - 1.5(-4/6)

x = -3 + 1

x = -2.

The exact solution is (-2, -4/6).

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The points where the inequality x+ 5y <-30 intercepts is ( 30, 0 ) and (0,6).

Here given the inequality.

x + 5y ≤ 30

To find the x-intercepts.

We have to substitute 0 for y and solve x to determine the x-intercepts.

x + 5 × 0 = 30

By solving the equation.

x = 30

( 30, 0 ) is the x-intercepts.

To find the y-intercepts.

By substituting 0 for x and solving y will get the y-intercept(s).

0 + 5y = 30

5y =30

y = 30/5

y = 6

In the point form, y-intercept.

Y-intercept(s): ( 0, 6 )

(30, 0) is the x-intercept.

Y-intercepts at : ( 0, 6 ).

The points in which the inequality x+ 5y <-30 intercepts is (30, 0) and (0,6).

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First:

Quotient: [tex]2x^{2} -11x+58[/tex]

Remainder: [tex]-294[/tex]

Second:

Quotient: [tex]x^{3} -5x^{2} +17x-83[/tex]

Remainder: [tex]422[/tex]

Third:

Quotient: [tex]2x-3[/tex]

Remainder: [tex]12[/tex]

Sam passed the marker of 483 miles, in 6 hours.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
An expression is given as M = 58h + 135. shows how many miles the same has traveled for h hours,
To evaluate the mile marker that sam passed at 6 hours, substitute the value with h in a given expression.
M = 58×6 +135

Simplifying the above expression gives the mile marker
M = 483 miles

Thus, the required miles are 483.

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Answer:

y=5x−2

I hope this helps!

Answer:

1/2

Step-by-step explanation:

Since 5 is one of the six possible numbers available, rolling a 5 is a 1/6 probability.

Since rolling a number less than 3 means rolling a 1 or 2, rolling a 1 or 2 is a 2/6 probability.

Add those probabilities up since you can get either of those outcomes and you get 1/6+2/6=3/6

3/6=1/2

The cost of one liter of washing up liquid would be = $1.8

Liters is a variable that is can be used to denote the measurement of a liquid.

The quantity of the washing up liquid that was given= 1.5 liters.

The cost of 1.5 liters of washing up liquid =$2.70

If 1.5 L = 2.70

1 L = X

Make X the subject of formula;

X = 1× 2.70/1.5

X = $1.8

Therefore, the cost of one liter of washing up liquid would be = $1.8

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The function g(x) = (x - 5)² has a translation of 5 units to the right.

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over x-axis, (-x, y).

-f(x) = Reflection over y-axis, (x, -y).

The parent function is a quadratic f(x) = x².

Now, The transformed function g(x) = (x - 5)² is a horizontal transformation of 5 units to the right.

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The probability that we will draw 4 kings from the 52-card deck be 1/270725.

Given, we draw 4 cards from a standard 52-card deck

we have to find the probability that we draw 4 kings

As, we know that the deck of cards contain 4 kings of two red and two black.

we have to choose 4 kings from 4 kings in the deck

Number of ways to choose 4 kings from the deck of cards =  C(4 , 4)

Now, total number of ways in which 4 cards can be chosen be,

C(52 , 4)

So, the probability of drawing 4 kings from the deck of cards be,

P(E) = C(4 , 4)/C(52 , 4)

P(E) = 4×3×2 / 52×51×50×49

P(E) = 1 / 13×17×25×49

P(E) = 1/270725

Hence, the required probability be 1/270725

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Answer:

The last answer is correct

Step-by-step explanation:

3x = 24  Divide both sides by 3

x = 8

A pair of shoes cost $8

Answer:

1: B

2: A

3: D

4: A

5: A, B

Step-by-step explanation:

1: 6/5 is 1.2 2/10 is 1/5

2: 6/14= 3/7 or 6/14

3: 3/12 is 1/4 or 3/12

4: 28/13 is 2 2/13

5: 35/6 which is also 2 3/16

#/# means divide so 35/6 is 35 divided by 6

Therefore , the probability that she selects none of those containing errors is 0.6798.

Calculating how likely or "possible" it is for an event to occur is the subject of probability. Words like "definitely," "impossible," or "likely" may be used to communicate the likelihood that a particular event will occur. Mathematics always expresses probabilities as fractions, decimals, or percentages, with values ranging from 0 to 1.

Here,

Number of ways of selecting 3 returns out of 59 is C(59,3).

Out of 59 returns, 59-7 = 52 returns has no error so number of ways of selecting 3 returns out fo 52 is C(52,3).

The probability that she selects none of those containing errors is

P( No errors )=[tex]\frac{C(52,3)}{C(59,3)}[/tex]=0.6798

Therefore , the probability that she selects none of those containing errors is 0.6798.

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The value of a comic book in dollars has been found to be 0.20y + 1.50, where y is the number of years since it was released. is  

(a)  [tex]0.2$[/tex]

(b) [tex]1.5$[/tex]

[tex]0.2 y+1.5 \longleftarrow \text { initial value }[/tex]

[tex]when $y$ increase one. the value increase $\$ 0.2$[/tex]

Travelling to movies and television programmes. An element of a comic book being in a popular film or television programme is a major factor in its value rising. Characters' comic book appearances have become far more valuable as they are integrated into the Marvel Cinematic Universe.

Marvel's first comic book just sold for $1.26m. Movies have contributed to the enduring popularity of superheroes, bringing in new audiences. The printed comic is still big business, worth over $1bn in North America alone.

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z-score of a value is  -5.96

What is z-score in binomial distribution?

The Z score represents the number of standard deviations above or below the mean. The Z score of the mean is 0 by definition.

What is Probability?

The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions.

Given,

A random variable, let's call it X, has parameters that fit the Binomial distribution: n (number of trials) = 50 and p (success probability) 0.76.

We must ascertain the z-score (Z) of the value 20 =  that this random variable X has chosen.

Now, for a random variable, say X, its z-score (Z) is defined as ,

Z = (X - mean of X)/ Standard deviation of X

A binomial random variable with the parameters once more n and p, its mean is given as np and its standard deviation is given as [tex]\sqrt{n*p*(1-p)}[/tex]

The standard deviation of X is provided as [tex]\sqrt{50*0.76*0.24}[/tex] = [tex]\sqrt{9.12}[/tex] = 3.0199933  while the mean of X is given as 50*0.76 = 38.

Therefore, the required z-score (Z) for X = 20, is given as,

Z = 20-38/3.0199933

Z= -5.9602781238

Z= -5.96 that is the necessary z-score.

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Answer:

[tex]x < -7[/tex]

Step-by-step explanation:

First subtract 2 from both sides.

[tex]-5x+2-2 > 37-2[/tex]

[tex]-5x > 35[/tex]

Then divide both sides by -5.

[tex]\frac{-5x}{-5} > \frac{35}{-5}[/tex]

For x < - 7, the inequality {- 5x + 2 > 37} is satisfied.

Given is the inequality as follows -

- 5x + 2 > 37

The given inequality is -

- 5x + 2 > 37

- 5x + 2 > 37

- 5x + 2 - 2 > 37 - 2

- 5x > 35

x < - 7

Therefore, for x < - 7, the inequality {- 5x + 2 > 37} is satisfied.

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Answer: the answer is 21

Step-by-step explanation:

If one angle measures 170°, and another angle measures (6k + 44)° and both are vertical angles that means the second angle should be the same as the first angle.

Vertical angles are congruent meaning they have an equal measure.

Now we have to find k

(6k + 44) = 170

subtract 44 - 44 and 170 - 44

(6k) = 126

divide 6 by 6, that leaves with just k on the left.

126 divided by 6  equals to 21

k = 21

Hope this helps!

The required percent decrease in the price of the skateboard is 40%.

What is the percentage?

A % is a number that indicates how many out of 100 it is, and it can also be expressed as a decimal or a fraction. Put the percentage value in the numerator and 100 in the denominator to convert a percentage to a fraction.

Here, we have

Original price = $84.50

sale price = $50.70

Percent decrease = 84.50-50.70/84.50 × 100 = 40%

Hence, the required percent decrease in the price of the skateboard is 40%.

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Answer:

10 years old

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

Y is midpoint of WR.

Hence,

YR = 1÷2 of WR ( Half of WR )

So,

WR = 2YR

= 2×11

= 22

Answer: Y=mx+b

Step-by-step explanation:

By hypothesis testing, The chef believes the complaint rate is less than 8%, when in fact it is not less than 8%. The chef continues to use the new recipe but experiences a large number of unsatisfied customers.

What does testing your hypotheses mean?

To make inferences about a population parameter or population probability distribution, a statistical process known as hypothesis testing analyzes data from a sample.

               First, a hazy assumption about the parameter or distribution is made.

What is hypothesis testing, and how can it be used?

A statistician will test a hypothesis about a population parameter in a process known as hypothesis testing. The type of data used in the study and its purpose will determine the methodology the analyst uses.

                     The plausibility of a hypothesis is evaluated using sample data in a process known as hypothesis testing.

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The original price of the instrument is $60.

Discount Price:

50% of 120 = 50/100 * 120

                   = 0.5 * 120

                   = 60

Original Price = Sale Price - Discount Price                  

                       = 120 - 60

                       = 60

Therefore, the original price of the instrument is $60.

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As AB is the perpendicular bisector of IK so we conclude that the right option is AJ=BJ.

A precise drawing in which a line is split in half by another line that is at a 90-degree angle to the original line is known as a perpendicular bisector. To divide into two equal portions is to bisect. When two lines intersect at a straight angle, they are perpendicular.

A line that precisely divides a line segment connecting two locations in half at a 90 degree angle is known as a perpendicular bisector. Finding the midpoint and negative reciprocal of two points, then entering these solutions into the equation for a line in slope-intercept form, will get the perpendicular bisector of the two points.

Option J can not be true as A can not be the midpoint of IK as A is not on IK.  Because J is on the IK as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. Hence, J is assumed as the midpoint of IK.

Option H i.e IJ = JK can not be true because AJ does not necessarily equal to BJ.

Option G i.e m∠IAJ  also does not true necessarily true. The reason is simple i.e AJ is arbitrary.

So, Option f i.e AJ = BJ is the correct Answer as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. So it can be assumed that that J is the midpoint as but it doesn't necessarily mean that IJ = JK, also it is true that perpendicular lines meet at 90 degree. Hence, statement F i.e AJ = BJ  is true.

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As AB is the perpendicular bisector of IK so we conclude that the right option is AJ=BJ.

What is perpendicular bisector?

A precise drawing in which a line is split in half by another line that is at a 90-degree angle to the original line is known as a perpendicular bisector. To divide into two equal portions is to bisect. When two lines intersect at a straight angle, they are perpendicular.

What is the perpendicular of two points?

A line that precisely divides a line segment connecting two locations in half at a 90 degree angle is known as a perpendicular bisector. Finding the midpoint and negative reciprocal of two points, then entering these solutions into the equation for a line in slope-intercept form, will get the perpendicular bisector of the two points.

Option J can not be true as A can not be the midpoint of IK as A is not on IK.  Because J is on the IK as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. Hence, J is assumed as the midpoint of IK.

Option H) i.e IJ = JK can not be true because AJ does not necessarily equal to BJ.

Option G)  i.e  m∠IAJ  also does not true necessarily true. The reason is simple i.e AJ is arbitrary.

So, Option f)  i.e AJ = BJ is the correct Answer as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. So it can be assumed that that J is the midpoint as but it doesn't necessarily mean that IJ = JK, also it is true that perpendicular lines meet at 90 degree. Hence, statement F i.e AJ = BJ  is true.

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Answer: point form: (4,3) equation form: x=4 y=3

Step-by-step explanation:

The carbinet has rectangular floor plan where the length is equal to 5 feet more than twice the width.  The the expression that represents the area in square feet is Option B 2w²+5. ∧where w is the width

The area of the rectangle is the floor space the rectangle can occupy at a given time.

The given parameters are

L= 2w+5

The width = w

Then area is given by the formula

A=L*W

A=2w*w+5

Simplify the expression you have

A=2w²+5 where w is the width

Therefore the area is b. 2w²+5, where w is the width

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The labeled quadrants in the standard xy coordinate plane is Quadrant II

What is Quadrants?

The intersection of the x-axis (the horizontal number line) and the y-axis in the cartesian system divides the coordinate plane into four equal pieces (the vertical number line). Because each of these four areas occupies a quarter of the entire coordinate plane, they are collectively referred to as quadrants.

Concept:

The x and y coordinates are both positive in quadrant I. In quadrant II, the x and y coordinates are oppositely positive. The x and y coordinates are both negative in quadrant III. The x-coordinate is positive and the y-coordinate is negative in quadrant IV.

The origin, or the point where the x- and y-axes connect, is where both the x and y coordinates are zero (0, 0).

The point is in the first quadrant if both x and y are positive. If both x and y are negative, the point will be in the second quadrant. In the third quadrant if both x and y are negatives, the point is located.

The labeled quadrants in the standard xy coordinate plane is Quadrant II

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A z-score tell us about an individual observation in a data set is, the number of standard deviations an observation is away from the mean.

The value of the z-score tells you how many standard deviations you are away from the mean. If a z-score is equal to 0, it is on the mean. A positive z-score indicates the raw score is higher than the mean average. For example, if a z-score is equal to +1, it is 1 standard deviation above the mean.

A z-score is the value of an observation expressed in standard deviation units. The sign of the score indicates whether it is above (positive) or below (negative) the mean, and the value quantifies how many standard deviations the score is from the mean.

The purpose of z-scores is to identify and describe the exact location of each score in a distribution & to standardize an entire distribution to understand & compare scores from different tests.

Z-scores or Z-statistics represent a statistical technique of measuring the deviation of data from the mean. There are different formula used for Z-score or Z-statistics depending upon what is measured. Z-statistics is generally used with Z-test which is a hypothesis testing statistical technique.

Therefore,

A z-score tell us about an individual observation in a data set is, the number of standard deviations an observation is away from the mean.

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Answer:

2 1/4

Step-by-step explanation:

I know bc its basic math

The value of y= 5.49≈ 5.5cm

What is 30-60-90 traingle?

The 30-60-90 triangle is cut straight through the middle along its altitude, like one half of an equilateral triangle. Its name is derived from its three angles of 30 degrees, 60 degrees, and 90 degrees. Any triangle with angles of 30-60-90 will look like this: The hypotenuse is always twice as long as the shortest leg, and the length of the long leg can be calculated by multiplying the short leg by the square root of three. The shortest leg is across from the 30-degree angle.

By 30-60-90 triangle rule,

Side across 60° angle = x

Hypotenuse side = 2x= 15

Side across 30° angle = x√3

By solving,

2x= 15

x= 7.5cm

So side across 60° angle= 7.5 cm

Side across 30° angle = 7.5×√3

                                     = 7.5× 1.732= 12.99≈ 13cm

As the figure given us square so,

13= 7.5+y

y= 13-7.5

y= 5.5 cm

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