Sandy is working with a carpenter to frame a house. They are using 8-foot-long boards, but each board must be cut to be 7 feet inches long. How much is cut off each board? Note: 1 foot = 12 inches A. 1 1/4 inches B. 1 3/4 inches C. 7 inches D. 3/4 inch

Answer:

A. y=-1/4x

Step-by-step explanation:

We have the information 3y=12x-9, the lines are perpendicular, and the new line passes through (-4,1). First, you want to put the original equation into slope intercept form by isolating the y, to do this we need to divide everything by 3 to get y=4x-3. The slopes of perpendicular lines are negative reciprocals so you need to find the negative reciprocal of 4, so flip it to 1/4 and multiply by -1, we get the slope of the new line as -1/4. So far we have the equation y=-1/4x+b. We are given a point on the line, (-4,1), we can plug these into the equation as x and y to solve for the y-intercept, b. You set it up as 1=-1/4(-4)+b. First you multiply to get 1=1+b, then you subtract 1 from both sides to isolate the variable and you get b=0. Then you can use b to complete your equation with y=-1/4x, or letter A.

Answer:

0

Step-by-step explanation:

multiply the negative thru the right part of the equation so, 5j+5-5j-5. The 5j and the 5 than cancel out with each other. Hope this helps!

Answer:

0

Explanation:

step 1 - remove the parenthesis from the expression

(5j + 5) - (5j + 5)

5j + 5 - 5j - 5

step 2 - combine like terms

5j + 5 - 5j - 5

5j - 5j + 5 - 5

0 + 0

0

therefore, the simplified form of the given expression is 0.

Answer:

We can use the cross products property.

11/8 = y / 13

8y = 11 * 13

y = 11 * 13 / 8 = 17.875

Answer:

y=17.875

Step-by-step explanation:

[tex]\frac{11}{8} = \frac{y}{13}[/tex]

11(13)=8y

143=8y

y=17.875

Answer:

(7, 5.25) lies on the graph.

Step-by-step explanation:

We are given the following values

x = 4,   6,  8, 12 and corresponding y values are:

y = 3, 4.5, 6, 9

Let us consider two points (4, 6) and (6, 4.5) and try to find out the equation of line.

Equation of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given as:

[tex]y=mx+c[/tex]

where m is the slope.

(x,y) are the coordinates from where the line passes.

c is the y intercept.

Here,

[tex]x_{1} = 4\\x_{2} = 6\\y_{1} = 3\\y_{2} = 4.5[/tex]

Formula for slope is:

[tex]m = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m = \dfrac{4.5-3}{6-4}\\\Rightarrow m = \dfrac{1.5}{2}\\\Rightarrow m = \dfrac{3}{4}[/tex]

Now, the equation of line becomes:

[tex]y=\dfrac{3}{4}x+c[/tex]

Putting the point (4,3) in the above equation to find c:

[tex]3=\dfrac{3}{4}\times 4+c\\\Rightarrow 3=3+c\\\Rightarrow c =0[/tex]

So, final equation of given function is:

[tex]y=\dfrac{3}{4}x[/tex]

OR

[tex]4y=3x[/tex]

As per the given options, the point (7, 5.25) satisfies the equation.

So correct answer is [tex](7, 5.25)[/tex].

Answer:

16 ounces = 1 pound

Step-by-step explanation:

You would just do 18/16 = 1.125 pounds. There are always 16 ounces in a pound, so it always works like this

Answer:

Question 2

Step-by-step explanation:

2) The time when she woke up was -  3° C

During nature walk, temperature got 3° C warmer than when she woke up.

So, temperature during nature walk = - 3 + 3 = 0° C

Answer:

5x + 10 = 25

Subtract 10 on each side to make x alone

5x = 15

divide by 5 on each side

x=3 so x=3

3x + 12 = 48

48-12=36

3x=36

divide by 3

x=12

4x + 8 = 16

4x = 8

x=2

2x + 15=25

2x=10

x=5

5x + 20 = 50

5x=30

x=6

hope this helps

1. 3

2.12

3.2

4.5

5.6

Step-by-step explanation:

Answer:

Step by step explanation

First:

Solution,

1. 5x + 10 = 25

Move constant to the R.H.S and change its sign:

5x = 25 - 10

Calculate the difference

5x = 15

Divide both sides by 5

5x/5 = 15/5

calculate

X = 3

2. 3x + 12 = 48

or, 3x = 48 - 12

or, 3x = 36

or, 3x/x = 36/3

x = 12

3. 4x + 8 = 16

or, 4x = 16 - 8

or, 4x = 8

or, 4x/x = 8/4

x = 2

4. 2x + 15 = 25

or, 2x = 25 - 15

or, 2x = 10

or, 2x/x= 10/2

x = 5

5. 5x + 20 = 50

or, 5x = 50-20

or, 5x = 30

or, 5x/x = 30/5

x = 6

Hope this helps...

Good luck on your assignment...

Answer:

When describing a property line drawn down the center of a creek bed

Answer:

See explanation

Step-by-step explanation:

To determine whether each of these functions is [tex]O(x^2)[/tex], we apply these theorems:

(a)Given the function: f(x)=100x+1000

The highest power of n is 1.

Therefore f(x) is O(x).

Since any O(x) function is always [tex]O(x^2)[/tex], 100x+1000 is [tex]O(x^2)[/tex].

[tex](b) f(x)=100x^ 2 + 1000[/tex]

The highest power of n is 2.

Therefore the function is [tex]O(x^2)[/tex].

Answer:

i think its 2000

Step-by-step explanation:

Answer:

(A)Step 1; it should be m∠m + m∠n + m∠o = 180 degrees (sum of angles in a triangle)

Step-by-step explanation:

The steps followed by the student are:

Step 1: m∠m + m∠n + m∠p = 180 degrees (sum of angles of a triangle)

Step 2: m∠p + m∠o = 180 degrees (adjacent supplementary angles)

Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p

Step 4: So, m∠m + m∠n = m∠p

We observe that the student made a mistake in Step 1, it should be m∠m + m∠n + m∠o = 180 degrees (sum of angles in a triangle).

p is outside the triangle, therefore it cannot form one of the angles in the triangle.

Answer:

Option (A).

Step-by-step explanation:

The function f(x) = x² + 4 is defined over the interval (-2, 2)

Total number of equal parts between this interval = 5

If the interval is divided into n equal parts, height of the right endpoint of each rectangle = [tex]\frac{5}{n}[/tex]

Height of the endpoint of the k rectangles = [tex]k.\frac{5}{n}[/tex]

Therefore, height of the endpoint of the kth rectangle = Height of first rectangle + height of k rectangles

= -2 + [tex]k.\frac{5}{n}[/tex]

Option (A). will be the answer.

The height of the right endpoint of the kth rectangle h = -2 + k (5/n)

The height is a vertical distance between two points. In the case of the triangle, the height will be the distance between the base and the top vertex of the triangle.

The function f(x) = x² + 4 is defined over the interval) (-2, 2 )

Total number of equal parts between this interval = 5

If the interval is divided into n equal parts, the height of the right endpoint of each rectangle = (5/n)

Height of the endpoint of the k rectangles = k (5/n)

The height of the endpoint of the kth rectangle:-

= Height of first rectangle + height of k rectangles

= -2   +  k (  5/n )

Therefore the height of the right endpoint of the kth rectangle h = -2 + k (5/n)

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Answer:

(a)0.5

(b)0.17

(c)0.625

(b)0.375

Step-by-step explanation:

Pr(E)=0.6​

Pr(F)=0.2

[tex]Pr(E\cap F)=0.1.[/tex]

(a)Pr (E|F )

[tex]Pr (E|F )=\dfrac{Pr(E \cap F)}{Pr(F)} \\=\dfrac{0.1}{0.2}\\\\=0.5[/tex]

(b)Pr (F|E )

[tex]Pr (F|E )=\dfrac{Pr(E \cap F)}{Pr(E)} \\=\dfrac{0.1}{0.6}\\\\=0.17[/tex]

(c)Pr (E|F')​

Pr(F')=1-P(F)

=1-0.2=0.8

[tex]Pr(E \cap F')=P(E)-P(E\cap F)\\=0.6-0.1\\=0.5[/tex]

Therefore:

[tex]Pr (E|F' )=\dfrac{Pr(E \cap F')}{Pr(F')} \\=\dfrac{0.5}{0.8}\\\\=0.625[/tex]

(d)Pr(E'|F')​

[tex]P(E'\cap F')=P(E \cup F)'\\=1-P(E \cup F)\\=1-[P(E)+P(F)-P(E\cap F)]\\=1-[0.6+0.2-0.1]\\=1-0.7\\=0.3[/tex]

Therefore:

[tex]Pr (E'|F' )=\dfrac{Pr(E' \cap F')}{Pr(F')} \\=\dfrac{0.3}{0.8}\\\\=0.375[/tex]

Answer:

B

Step-by-step explanation:

A is not a function because the same x value is repeated twice with different y values. The same goes for C and D so the answer is C.

Answer:

B.

Step-by-step explanation:

Well a relation is a set of points and a function is a relation where every x value corresponds to only 1 y value.

So lets see which x values in these relations have only 1 y value.

A. Well a isn’t a function because the number 3 which is a x value had two y values which are -1 and 4.

B. This relation is a function because there are no similar x values.

C. This is not a function because the x value 4 has two y values which are 4 and -3.

D. This is not a function because the number 1 has 2 and 3 as y values.

━━━━━━━☆☆━━━━━━━

▹ Answer

0.25 = 1/4 because 25/100 = 1/4

▹ Step-by-Step Explanation

0.25 to a fraction → 25/100

25/100 = 1/4

Therefore, this statement is true. (0.25 = 1/4 because 25/100 = 1/4)

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

[tex]\dfrac{1}{7}[/tex]

Step-by-step explanation:

There are 7 days in a week.

For the first person, we select one day out of the 7 days. The first person has 7 options out of the 7 days.

Let Event A be the event that the first person was born on a day of the week.

Therefore:

[tex]P(A)=\dfrac{7}{7}=1[/tex]

The second person has to be born on the same day as the first person. Therefore, the second person has 1 out of 7 days to choose from.

Let Event B be the event that the second person was born.

Therefore, the probability that the second person was born on the same day as the first person:

[tex]P(B|A)=\dfrac{1}{7}[/tex]

By the definition of Conditional Probability

[tex]P(B|A)=\dfrac{P(B \cap A)}{P(A)} \\$Therefore:\\P(B \cap A)=P(B|A)P(A)[/tex]

The probability that both were born on the same day is:

[tex]P(B \cap A)=P(B|A)P(A) = \dfrac{1}{7} X 1 \\\\= \dfrac{1}{7}[/tex]

Answer: D

Step-by-step explanation:

According to the question, Silver Lake has a population of 114,000. The population is decreasing at a rate of 1.5% each year

The initial population Po = 114000

Rate = 1.5% = 0.015

The declining population formula will be:

P = Po( 1 - R%)x^2

The decay formula

Since the population is decreasing, take away 0.015 from 1

1 - 0.015 = 0.985

Substitutes all the parameters into the formula

P(s) = 114000(0.985)x^2

P(s) = 114000× 0985x^2

The correct answer is written above.

Since option A does not have square of x, we can therefore conclude that the answer is D - non of the choices is correct.

Answer:

x = 0,00375 mm

Step-by-step explanation:

a) El factor de ampliación es 400/1   es decir el tamaño real se verá ampliado 400 veces mediante el uso del microscopio

b) De acuerdo a lo establecido en la respuesta a la pregunta referida en a (anterior) podemos establecer una regla de tres, según:

Si al microscopio el tamaño de la célula es 1,5 mm, cual será el tamaño verdadero ( que es reducido 400 en relación al que veo en el microscopio)

Es decir     1,5 mm      ⇒    400

                    x (mm)    ⇒       1 (tamaño real de la célula)

Entonces

x  =  1,5 /400

x = 0,00375 mm

Answer:

The equation for this ellipse is [tex]\frac{x^{2}}{64} + \frac{y^{2}}{16} = 1[/tex].

Step-by-step explanation:

The standard equation of the ellipse is described by the following expression:

[tex]\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}} = 1[/tex]

Where [tex]a[/tex] and [tex]b[/tex] are the horizontal and vertical semi-axes, respectively. Given that major semi-axis is horizontal, [tex]a > b[/tex]. Then, the equation for this ellipse is written in this way: (a = 8, b = 4)

[tex]\frac{x^{2}}{64} + \frac{y^{2}}{16} = 1[/tex]

The equation for this ellipse is [tex]\frac{x^{2}}{64} + \frac{y^{2}}{16} = 1[/tex].

Answer:

(a) The value of a is 53.35.

(b) The value of a is 38.17.

(c) The value of a is 26.95.

(d) The value of a is 25.63.

(e) The value of a is 12.06.

Step-by-step explanation:

The probability density function of X is:

[tex]f_{X}(x)=\frac{1}{55-22}=\frac{1}{33}[/tex]

Here, 22 < X < 55.

(a)

Compute the value of a as follows:

[tex]P(X\leq a)=\int\limits^{a}_{22} {\frac{1}{33}} \, dx \\\\0.95=\frac{1}{33}\cdot \int\limits^{a}_{22} {1} \, dx \\\\0.95\times 33=[x]^{a}_{22}\\\\31.35=a-22\\\\a=31.35+22\\\\a=53.35[/tex]

Thus, the value of a is 53.35.

(b)

Compute the value of a as follows:

[tex]P(X< a)=\int\limits^{a}_{22} {\frac{1}{33}} \, dx \\\\0.95=\frac{1}{33}\cdot \int\limits^{a}_{22} {1} \, dx \\\\0.49\times 33=[x]^{a}_{22}\\\\16.17=a-22\\\\a=16.17+22\\\\a=38.17[/tex]

Thus, the value of a is 38.17.

(c)

Compute the value of a as follows:

[tex]P(X\geq a)=\int\limits^{55}_{a} {\frac{1}{33}} \, dx \\\\0.85=\frac{1}{33}\cdot \int\limits^{55}_{a} {1} \, dx \\\\0.85\times 33=[x]^{55}_{a}\\\\28.05=55-a\\\\a=55-28.05\\\\a=26.95[/tex]

Thus, the value of a is 26.95.

(d)

Compute the value of a as follows:

[tex]P(X\geq a)=\int\limits^{55}_{a} {\frac{1}{33}} \, dx \\\\0.89=\frac{1}{33}\cdot \int\limits^{55}_{a} {1} \, dx \\\\0.89\times 33=[x]^{55}_{a}\\\\29.37=55-a\\\\a=55-29.37\\\\a=25.63[/tex]

Thus, the value of a is 25.63.

(e)

Compute the value of a as follows:

[tex]P(1.83\leq X\leq a)=\int\limits^{a}_{1.83} {\frac{1}{33}} \, dx \\\\0.31=\frac{1}{33}\cdot \int\limits^{a}_{1.83} {1} \, dx \\\\0.31\times 33=[x]^{a}_{1.83}\\\\10.23=a-1.83\\\\a=10.23+1.83\\\\a=12.06[/tex]

Thus, the value of a is 12.06.

Answer:

  [tex]\dfrac{4x^2+12x+5}{6x^2-3x}[/tex]

Step-by-step explanation:

Invert the denominator and multiply.

  [tex]\dfrac{2x+5}{3x}\div\dfrac{2x-1}{2x+1}=\dfrac{2x+5}{3x}\cdot\dfrac{2x+1}{2x-1}\\\\=\dfrac{(2x+5)(2x+1)}{(3x)(2x-1)}=\boxed{\dfrac{4x^2+12x+5}{6x^2-3x}}\qquad\text{matches choice A}[/tex]

Answer:

[tex]\frac{4x^2+12x+5}{6x^2-3x}[/tex]

Step-by-step explanation:

After using the reciprocal of the second term, the denominator will multiply out to be [tex]6x^2-3x[/tex]. There is only one option with that as the denominator so it must be the correct answer.

Answer:

81.23 ft and 77.88 ft long

Step-by-step explanation:

The sum of the internal angles of a triangle is 180 degrees, the missing angle is:

[tex]a+b+c=180\\a+23+22=180\\a=135^o[/tex]

According to the Law of Sines:

[tex]\frac{A}{sin(a)}= \frac{B}{sin(b)}= \frac{C}{sin(c)}[/tex]

Let A be the side that is 147 feet long, the length of the other two sides are:

[tex]\frac{A}{sin(a)}= \frac{B}{sin(b)}\\B=\frac{sin(23)*147}{sin(135)}\\B=81.23\ ft\\\\\frac{A}{sin(a)}= \frac{C}{sin(c)}\\C=\frac{sin(22)*147}{sin(135)}\\C=77.88\ ft[/tex]

The other two sides are 81.23 ft and 77.88 ft long

Answer:

One solution

Step-by-step explanation:

99% of the time, linear equations (equations that have the first degree) have only one solution. However, it's always good to check.

6 - 3x = 12 - 6x

6 = 12 - 3x

-3x = -6

x = 2

As you can see, only one solution. Hope this helps!

Behold the quotient of F and the product of r,s, and T:  F / (r·s·T)

The numerical of the statement the quotient of F and the product of r,s, and T is F/(r×s×T).

The number which is being divided is the dividend.

The number with which we are dividing is the divisor.

The result when a dividend is divided by the divisor is the quotient.

A remainder is the extra portion of a number when it isn't completely divisible.

Given, Are some variables F, r, s, and t.

Now, The product of r,s, and T is,

= r×s×T and the complete statement the quotient of F and the product of r,s, and T can be written as,

F/(r×s×T).

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Answer:

  C)  42

Step-by-step explanation:

The parallel lines divide the transversals proportionally.

  x/35 = 30/25

  x = 35(6/5) . . . . multiply by 35, reduce the fraction

  x = 42

Answer:

Hey there!

There are a few ways you could solve this problem, but the easiest would to be writing an equation.

You could say-

2.3x=69

Divide by 2.3

x=30

Hope this helps :)

Answer:

30

Step-by-step explanation:

the answer is 30 bc increasing something by 130% is multiplying it by 2.3 so technically you have to divide 69 by 2.3 which equals to 30

Answer:

Step-by-step explanation:

Let x represent the length of the side not parallel to the partition. Then the length of the side parallel to the partition is ...

  y = (300 -2x)/3

And the enclosed area is ...

  A = xy = x(300 -2x)/3 = (2/3)(x)(150 -x)

This is the equation of a parabola with x-intercepts at x=0 and x=150. The line of symmetry, hence the vertex, is located halfway between these values, at x=75.

The maximum area is enclosed when the dimensions are ...

  50 ft by 75 ft

That maximum area is 3750 square feet.

_____

Comment on the solution

The generic solution to problems of this sort is that half the fence (cost) is used in each of the orthogonal directions. Here, half the fence is 150 ft, so the long side measures 150'/2 = 75', and the short side measures 150'/3 = 50'. This remains true regardless of the number of partitions, and regardless if part or all of one side is missing (e.g. bounded by a barn or river).

Answer: 29,000.00

Step-by-step explanation:

Let the income=x.  22%=0.22.

So 6380/x=0.22

x=6380/0.22=29,000.00

Answer:

The frequency table is shown below.

Step-by-step explanation:

The data set arranged ascending order is:

S = {33 , 34 , 39 , 48 , 49 , 50 , 53 , 54 , 55 , 56 , 58 , 58,  60 , 63 , 64 , 65 , 70 , 71 , 74 , 84}

It is asked to use the minimum value from the data set as the lower class limit for the first row.

So, the lower class limit for the first class interval is 33.

To determine the class width compute the range as follows:

[tex]\text{Range}=\text{Maximum}-\text{Minimum}[/tex]

          [tex]=84-33\\=51[/tex]

The number of classes requires is 5.

The class width is:

[tex]\text{Class width}=\frac{Range}{5}=\frac{51}{2}=10.2\approx 10[/tex]

So, the class width is 10.

The classes are:

33 - 42

43 - 52

53 - 62

63 - 72

73 - 82

83 - 92

Compute the frequencies of each class as follows:

Class Interval                  Values                        Frequency

   33 - 42                      33 , 34 , 39                             3

   43 - 52                      48 , 49 , 50                            3

   53 - 62          53 , 54 , 55 , 56 , 58 , 58,  60              7

   63 - 72                 63 , 64 , 65 , 70 , 71                      5

   73 - 82                              74                                  1

   83 - 92                             84                                   1

   TOTAL                                                                   20

Compute the relative frequencies as follows:

Class Interval          Frequency        Relative Frequency

   33 - 42                        3                   [tex]\frac{3}{20}\times 100\%=15\%[/tex]

   43 - 52                        3                   [tex]\frac{3}{20}\times 100\%=15\%[/tex]

   53 - 62                        7                   [tex]\frac{7}{20}\times 100\%=35\%[/tex]

   63 - 72                        5                   [tex]\frac{5}{20}\times 100\%=25\%[/tex]

   73 - 82                         1                   [tex]\frac{1}{20}\times 100\%=5\%[/tex]

   83 - 92                         1                   [tex]\frac{1}{20}\times 100\%=5\%[/tex]

   TOTAL                        20                          100%

Answer:

5.35 more miles

Answer:

5.35 miles to the finish line

Step-by-step explanation:

Step one

13.1-7.75=

5.35

Answer:

a) Mean = 0.125 inch

Standard deviation = 0.13975 inch

b) Probability that the width of the casing minus the width of the door exceeds 1/4 inch = P(X > 0.25) = 0.18673

c) Probability that the door does not fit in the casing = P(X < 0) = 0.18673

Step-by-step explanation:

Let the distribution of the width of the casing be X₁ (μ₁, σ₁²)

Let the distribution of the width of the door be X₂ (μ₂, σ₂²)

The distribution of the difference between the width of the casing and the width of the door = X = X₁ - X₂

when two independent normal distributions are combined in any manner, the resulting distribution is also a normal distribution with

Mean = Σλᵢμᵢ

λᵢ = coefficient of each disteibution in the manner that they are combined

μᵢ = Mean of each distribution

Combined variance = σ² = Σλᵢ²σᵢ²

λ₁ = 1, λ₂ = -1

μ₁ = 24 inches

μ₂ = 23 7/8 inches = 23.875 inches

σ₁² = (1/8)² = (1/64) = 0.015625

σ₂ ² = (1/16)² = (1/256) = 0.00390625

Combined mean = μ = 24 - 23.875 = 0.125 inch

Combined variance = σ² = (1² × 0.015625) + [(-1)² × 0.00390625] = 0.01953125

Standard deviation = √(Variance) = √(0.01953125) = 0.1397542486 = 0.13975 inch

b) Probability that the width of the casing minus the width of the door exceeds 1/4 inch = P(X > 0.25)

This is a normal distribution problem

Mean = μ = 0.125 inch

Standard deviation = σ = 0.13975 inch

We first normalize/standardize 0.25 inch

The standardized score of any value is that value minus the mean divided by the standard deviation.

z = (x - μ)/σ = (0.25 - 0.125)/0.13975 = 0.89

P(X > 0.25) = P(z > 0.89)

Checking the tables

P(x > 0.25) = P(z > 0.89) = 1 - P(z ≤ 0.89) = 1 - 0.81327 = 0.18673

c) Probability that the door does not fit in the casing

If X₂ > X₁, X < 0

P(X < 0)

We first normalize/standardize 0 inch

z = (x - μ)/σ = (0 - 0.125)/0.13975 = -0.89

P(X < 0) = P(z < -0.89)

Checking the tables

P(X < 0) = P(z < -0.89) = 0.18673

Hope this Helps!!!