seven less than the quotient of nineteen and a number

Answer:

2b)x=1/3 or x= -4

2c) x= 0 or x= -2/3

Step-by-step explanation:

To factor ax² + bx + c, use the AC method.

(b) 3x² + 11x − 4 = 0

(3x − 1) (x + 4) = 0

3x − 1 = 0, or x + 4 = 0

x = 1/3, or x = -4

(c) 12x² + 8x = 0

Here, you can simply factor the greatest common factor, 4x.

4x (3x + 2) = 0

4x = 0, or 3x + 2 = 0

x = 0, or x = -2/3

Step-by-step explanation:

[tex]15( \frac{11\pi}{6} ) \\ 15 \div 3 = 5 \\ 6 \div 3 = 2 \\ = 5( \frac{11\pi}{2} )[/tex]

[tex]11 \times 5 \\ = \frac{55\pi}{2} [/tex]

Answer:

There is no sufficient evidence to support the claim that the bags are underfilled

Step-by-step explanation:

We are given;

n = 27 bags

Sample mean;X = 402 gram

Population mean;μ = 404 gram

Variance = 676

We know that, standard deviation(σ) = √variance

Thus;

σ = √676

σ = 26

The hypotheses are;

Null hypothesis; H0: μ = 404

Alternative hypothesis; HA: μ < 404

Let's find the z-score from the formula;

z = (X - μ)/(√σ/n)

z = (402 - 404)/√(26/27)

z = -2.04

From the z-distribution table attached, we have a p-value of 0.02068

This is less than the significance value of 0.01 and thus we will reject the null hypothesis and conclude that there is no sufficient evidence to support the claim that the bags are underfilled

On the first roll, you have a 1/3 probability of rolling a 1 or 2 and thus winning $200.

There's a 2/3 probability of not rolling a 1 or 2 on the first roll. On the second roll, there is again a 1/3 probability of rolling a 1 or 2, and 2/3 probability otherwise, so that there is a 1/3*2/3 = 2/9 probability of getting a 1 or 2 and thus winning $100, and 2/3*2/3 = 4/9 probability of losing.

(a) Let [tex]W[/tex] be a random variable representing the winnings from playing the game. It has the probability mass function

[tex]P(W=w)=\begin{cases}\frac13&\text{for }w=\$200\\\frac29&\text{for }w=\$100\\\frac49&\text{otherwise}\end{cases}[/tex]

(b) Compute the expected value of [tex]W[/tex]:

[tex]E[W]=\displaystyle\sum_w w\,P(W=w)=\$200\cdot\frac13+\$100\cdot\frac29+\$0\cdot\frac49\approx\$88.89[/tex]

Answer: it would be $96.25

Step-by-step explanation:

In the am, it’s 4 hours. 4x11= $44

In the pm it’s 4 hours and 45mins. 4x11=44

The for the 45 mins. Multiply 45x11= 495 then divide by 60. That gives you $8.25. When you add them all together, you get 96.25

Answer:

z > -5/2

Step-by-step explanation:

Since both sides are divided by a negative number, the equality is switched.

10 - 4z < 20

(10 - 4z) - 10 < 20 - 10

-4z < 10

(-4z)/-4 < 10/-4

z > -5/2

The solution for z will be;

⇒ z ∈ (- 2.5 , ∞ )

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is,

⇒ 10 - 4z < 20

Now,

Since, The inequality is,

⇒ 10 - 4z < 20

Solve for z as;

⇒ 10 - 4z < 20

⇒ 10 - 4z + 4z < 20 + 4z

⇒ 10 < 20 + 4z

⇒ 10 - 20 < 4z

⇒ - 10 < 4z

⇒ - 2.5 < z

⇒ z ∈ (- 2.5 , ∞ )

Thus, The interval notation is,

⇒ z ∈ (- 2.5 , ∞ )

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Answer: D. No; the graph fails the vertical line test.

The vertical line test is a tool used to determine if we have a function. If we can draw a single straight vertical line through more than one point on the red curve, then the graph is said to have failed the vertical line test. Consequently, this leads to the relation not being a function.

For this circle graph, we can draw a vertical line through more than one point, which is why we don't have a function here.

Put another way, there are inputs (x) that produce more than one output (y), so that's why we don't have a function.

The graph shows a function The graph fails the vertical line test.

A vertical line test is a tool used to determine if we have a function.

The vertical line test is a method that is used to determine whether a given relation is a function or not. The approach is rather simple.

If we can draw a single straight vertical line through more than one point on the red curve, then the graph is said to have failed the vertical line test.

Consequently, this leads to the relation not being a function.

For this circle graph, we can draw a vertical line through more than one point, which is why we don't have a function here.

Put another way, there are inputs (x) that produce more than one output (y), so that's why we don't have a function.

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Answer:

(-4, 3)

Step-by-step explanation:

From the graph, it looks like the two lines intersect at pint (-4, 3).

Answer:

142

Step-by-step explanation

A cluster is a small group of dots close together. An outlier is a single dot far away from the rest of the dots.

The above graph has a small cluster around y 6&7 and has an outlier at (9,5)

The answer should be D.

Answer:

The correct answer is D. This scatter plot has one cluster and one outlier.

Step-by-step explanation:

From looking at the scatterplot, the majority of the points are collected on the upper left side of the coordinate grid, creating a cluster.  This just means that these data points are located close to one another.

If we continue to look at the scatterplot, we can see that there is one data point at approximately (9, 5.25) that is very far from the other data points.  This point is considered to be an outlier because it does not follow the general trend of the other data points and changes the data analysis significantly if included in the calculations.

Hope this helped!

Answer:

∠ 2 = 45°

Step-by-step explanation:

∠ 1 and ∠ 2 are same- side interior angles and are supplementary, thus

∠ 2 = 180° - ∠ 1 = 180° - 135° = 45°

Answer: 45

Step-by-step explanation:

Answer:

- 3⁷/2⁹

Step-by-step explanation:

Answer:

The rectangle has a width of 4 and a height of 8

Step-by-step explanation:

Let the height of the rectangle be H and the width be W.

We know the height of the rectangle is twice the width, so:

H = 2W

The area of a rectangle, A, is given by A = W * H, so in this case:

32 = W * 2W

32 = 2W²

W² = 16

W = 4

Knowing that the width is 4, the height must be 8. This gives us an area of 32.

Answer:

y = In | cos(2x + c ) | + c

Step-by-step explanation:

y" + (y')^2 + 4 = 0

substituting u = y'

u' + u^2 + 4 = 0

hence : u' = - (u^2 + 4 )

       [tex]\frac{u'}{-(u^2 + 4)}[/tex] = 1 ------- (1)

integrating both sides of the equation 1

[tex]1/2 \int\limits^1_1 {\frac{2du}{(u^2+4)} } \, = x + c[/tex]

x + c = [tex]- \frac{1}{2} arc tan (\frac{u}{2} )[/tex]   hence  u = -2 tan(2x + c )

remember u = y'

y' = -2 tan(2x + c) ------ (2)

integrating both sides of the equation 2

y = ∫ [tex]\frac{-sin u}{cos u } du[/tex]

therefore Y = In | cosu | + c

 y = In | cos(2x + c ) | + c

Answer: (31.75%, 36.25%)

Step-by-step explanation:

Let p be the proportion of workers in this city who have full health insurance coverage.

As per given,

Sample size : n= 170

Number of workers who had full health insurance coverage.=578

i.e. sample proportion: [tex]\hat{p}=\dfrac{578}{1700}\approx0.34[/tex]

Also, z-score for 95% confidence level : 1.96

Formula to find the confidence interval for p :

[tex]\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

[tex]0.34\pm (1.96)\sqrt{\dfrac{0.34(1-0.34)}{1700}}[/tex]

[tex]=0.34\pm (1.96)\sqrt{0.000132}\\\\=0.34\pm (1.96)(0.011489125)\\\\\approx 0.34\pm0.0225\\\\=(0.34-0.0225,\ 0.34+0.0225)\\\\=(0.3175,\ 0.3625) =(31.75\%,\ 36.25\%)[/tex]

Hence, a 95% confidence interval for the true percent of workers in this city who have full health insurance coverage= (31.75%, 36.25%)

The circumference of a circle, which is another way of saying the perimeter of a circle, can be found using the formula 2πr.

Note that π represents the irrational number 3.14159... which

rounds to 3.14 and r represents the radius of the circle.

Therefore, since π = 3.14, another way of writing the formula

for the circumference of a circle is 2 · 3.14r or 6.28r.

Answer:

circumference = 2 π r

or

circumference = π d

Step-by-step explanation:

r = radius of a circle

d = diameter

therefore

circumference = 2 π r

or

circumference = π d

Answer:

Hope this will help you :)

Step-by-step explanation:

Answer:

I think it would be 8 and 1/3 inches long

Step-by-step explanation:

P.S. You spelled inches wrong

Answer:

{3x-2}+4=10

Step-by-step explanation:

Answer:

[tex]\sqrt{113\\[/tex]

Step-by-step explanation:

set the problem up like this:

[tex]\sqrt{(x2-x1)^{2} +(y2-y1)^2[/tex]

(x1,y1) (x2,y2)

x1=-3

y1+3

x2=5

y2=-4

The equation should look like this:

[tex]\sqrt{(5-(-3))^2 + (-4-3)^2[/tex]

Then you solve it and 113 is the square root in between.

Hope it helps...

Answer:

Step-by-step explanation:

Hello, please consider the following.

[tex]\displaystyle f'(0)=\lim_{x\rightarrow0} {\dfrac{f(x)-f(0)}{x-0}}\\\\=\lim_{x\rightarrow0} {\dfrac{\dfrac{\sqrt{1+x}-1}{x}-k}{x}}\\\\=\lim_{x\rightarrow0} {\dfrac{\dfrac{\sqrt{1+x}-1-kx}{x}}{x}}\\\\=\lim_{x\rightarrow0} {\dfrac{\sqrt{1+x}-1-kx}{x^2}}\\[/tex]

Thank you

Answer:

-2x-15=6x+9

-2x-6x=9+15

-8x=24

x=-24/8

x=-3

Answer:

Twelve tickets cost $30 --> True

Thirty tickets cost $12 --> False

Each additional costs $2.50 --> True

The table is a partial rep --> True

ordered pairs --> False

Step-by-step explanation:

Twelve tickets cost $30 --> True, you can literally see that in the table

Thirty tickets cost $12 --> False, 30 is not in the table so you don't have that information. Besides, $12 is an unlikely low value for so many tickets.

Each additional costs $2.50 --> True, you can see the difference in the TotalCost column to be consistently 2.50.

The table is a partial rep --> True, values below 11 are not shown for example.

ordered pairs --> False --> Then the x value should be first, e.g., (11, 27.50), since the cost y is a function of the number x.

Answer:

In 4 hours.

Step-by-step explanation:

Just equate f(x) = g(x). So:

15x + 90 = 30x + 30

60 = 15x

x = 4 hours.

In 4 hours the amount of candy produced be the same for both machines.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

It is given that A candy factory wants to compare a new machine to their current machine. Both machines produce y boxes of candy for every hour x. The current machine is represented by the equation f(x). The new machine is represented by the equation g(x). f(x) = 15x + 90 g(x) = 30x + 30.

The value of time will be calculated below:-

Just equate f(x) = g(x).

15x + 90 = 30x + 30

60 = 15x

x = 4 hours.

Therefore, In 4 hours the amount of candy produced is the same for both machines.

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Answer: C. The size of a business is​ ordinal-scaled because it has values that can be used as an order or rank of a categorical variable.

Step-by-step explanation: Ordinal variables are simply categorical in nature just like nominal variables, however, the difference exists in the fact that ordinal labels posses an ordered rank or level unlike nominal variables. Though the extent or width of the difference between these labels cannot be ascertained. In the scenario above, size of businesses are labeled qualitatively with labels such as : small, medium and large. This labels depicts and follow a certain order with small being the least, then medium, then large. Telling us large businesses are superior in size to small and medium and medium is superior to large. Though the extent of the difference cannot be accurately ascertained.

Answer:

Step-by-step explanation:

First we must understand that absolute value of a function returns both positive and negative function.

1) Given |x-6| = 5

For the positive value of the function:

x-6 = 5

Add 6 to both sides

x-6+6 = 5+6

x = 11

For the negative function:

-(x-6) = 5

Open the parentheses

-x+6 = 5

Subtract 6 from both sides

-x+6-6 = 5-6

-x = -1

x = 1

Hence x = 1, x = 11

2 ) Given |3x-7| = 12

For the positive value of the function:

3x-7 = 12

Add 7 to both sides

3x-7+7 = 12+7

3x = 19

x = 19/3

For the negative function:

-(3x-7) = 12

Open the parentheses

-3x+7 = 12

Subtract 7 from both sides

-3x+7-7 = 12-7

-3x = 5

x = -5/3

Hence x = 19/3, x = -5/3

3) Given |2x+9| - 10= 5

For the positive value of the function:

2x+9-10= 5

2x-1 = 5

Add 1 to both sides

2x-1+1 = 5+1

2x = 6

x= 3

For the negative function:

-(2x+9)-10 = 5

Open the parentheses

-2x-9-10 = 5

-2x-19 = 5

Add 19 to both sides

-2x-19+19 = 5+19

-2x= 24

x = -24/2

x= -12

Hence x = 3, x = -12

4) ) Given |5x-3|+12 = 4

For the positive value of the function:

5x-3+12= 4

5x+9 = 4

Subtract 9 from both sides

5x+9-9 = 4-9

5x = -5

x= -1

For the negative function:

-(5x-3)+12= 4

Open the parentheses

-5x+3+12 =4

-5x+15 = 4

Subtract 15 from both sides

-5x+15-15 = 4-15

-5x = -11

x = 11/5

Hence x = -1, x = 11/5

Answer:

x and y do not show direct variation

Step-by-step explanation:

Two quantities x and y show direct variation when

y = kx

and k ≠ 0

Given x = y + 2

Making y the subject of the formula:

y = x - 2

The equation above cannot be written in the form y = kx

This means that x and y are not in a proportional relationship

For instance, let's say when x = 4

y = (4) - 2 = 2

Now, if x is doubled, x = 8

y = (8) - 2 = 6

Therefore, doubling x does not necessarily double y, hence they are not in a direct variation.

Answer:

[tex]Length = \frac{64}{3}m[/tex]

[tex]Width= \frac{32}{3}m[/tex]

Step-by-step explanation:

Given

[tex]Perimeter = 64m[/tex]

[tex]Length = 2 * Width[/tex]

Required

Determine the length and the width

Since the alley is rectangular, the perimeter is as follows;

[tex]Perimeter = 2 (Length * Width)[/tex]

Substitute 64m for Perimeter

[tex]64m = 2(Length + Width)[/tex]

Substitute 2 * Width for Length

[tex]64m = 2(Width+ 2 * Width)[/tex]

[tex]64m = 2(Width+ 2 Width)[/tex]

[tex]64m = 2(3 Width)[/tex]

[tex]64m = 6Width[/tex]

Divide both sides by 6

[tex]Width= \frac{64m}{6}[/tex]

[tex]Width= \frac{32}{3}m[/tex]

Recall that

[tex]Length = 2 * Width[/tex]

[tex]Length = 2 * \frac{32}{3}m[/tex]

[tex]Length = \frac{64}{3}m[/tex]

Answer:

A.1.5 is the correct answer.

Answer:

A. 1.5

Step-by-step explanation:

End points of the line segment:

Length of line segment:

Half length of the line segment:

Midpoint is at same distance from either end:

Midpoint is 1.5