Jeff has a cube train that is 22 inches long. he removes 8 inches of cubes from the train. How long is Jeff's cube train now?

[tex]\bf \textit{Law of sines} \\\\ \cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{sin(75^o)}{17}=\cfrac{sin(D)}{10}\implies \cfrac{10sin(75^o)}{17}=sin(D) \\\\\\ sin^{-1}\left[ \cfrac{10sin(75^o)}{17} \right]=D\implies 34.6\approx D[/tex]

since all interior angles in a triangle must be 180°, that means that C = 180 - 75 - 34.6 = 70.4.  Let's find AD, which is the other sides pair length.

[tex]\bf \cfrac{sin(75^o)}{17}=\cfrac{sin(70.4^o)}{AD}\implies ADsin(75^o)=17sin(70.4^o) \\\\\\ AD=\cfrac{17sin(70.4^o)}{sin(75^o)}\implies AD\approx 16.58[/tex]

now, check the picture below, let's find the altitude of the parallelogram.

[tex]\bf sin(34.6^o)=\cfrac{\stackrel{opposite}{h}}{\stackrel{hypotenuse}{16.58}}\implies 16.58sin(34.6^o)=h\implies 9.4\approx h \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a parallelogram}\\\\ A=bh~~ \begin{cases} b=base\\ h=height\\ \cline{1-1} b=17\\ h=9.4 \end{cases}\implies A=(17)(9.4)\implies A=159.8[/tex]

Well it depends. If your radical is wrapped around the entire expression, then your answer would be 3xy²z²√10xz, but if your radical is ONLY wrapped around 90, then your answer would be 3√10x³y⁴z⁵ [radical wrapped ONLY around 10]. So, with the way this is written, although it is simple to figure this out, it is difficult to find the answer you are looking for.

Answer:

C [tex]11+13+15+17+...[/tex]

Step-by-step explanation:

Consider the series

[tex]\sum\limits_{n=3}^{\infty}(2n+5)[/tex]

The nth term of series is [tex]a_n=2n+5[/tex]

The bottom index tells you that n starts changing from 3, so

[tex]a_3=2\cdor 3+5=11\\ \\a_4=2\cdot 4+5=13\\ \\a_5=2\cdot 5+5=15\\ \\a_6=2\cdot 6+5=17\\ \\...[/tex]

Thus, the sum of all terms is

[tex]11+13+15+17+...[/tex]

Answer:

2/3

Step-by-step explanation:

The cube has the following numbers written on its faces;

1, 2, 3, 4, 5, 6

Among these numbers, the multiples of 2 and 3 are;

2, 3, 4, 6 .

The probability of rolling a multiple of 2 or 3 is thus;

4/6 = 2/3

Which is the required probability

Answer:

perpendicular is the opposite, so -3

Answer:

FIRST OPTION: -3

Step-by-step explanation:

By definition, if two lines are perpendicular to each other, then their slopes are negative reciprocals.

In this case you can observe that that the slope of the line is [tex]\frac{1}{3}[/tex] and you know that the other line is perpendicular to this line. Therefore, their slopes are negative reciprocals.

This means that:

If [tex]slope_1=\frac{1}{3}[/tex] ,then  [tex]slope_2=-3[/tex]

This matches with the first option.

Answer:

Step-by-step explanation:

Sample space {1,2,3,4,5,6}

3 to 6: {3,4,5,6}

My punctuation may not be the same as yours, but that is what they are asking for.

Answer:

y = 37/36

Step-by-step explanation:

let's take a peek at the denominators hmmmm 5, 9, 8   hmmmm we can get an LCD of simply their product, well, that'd be 360, so then, let's multiply both sides by the LCD of 360 to do away with the denominators and proceed.

[tex]\bf \cfrac{3}{5}y+\cfrac{2}{9}=\cfrac{5}{8}-\cfrac{2}{5}y+\cfrac{5}{8}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{360}}{360\left( \cfrac{3}{5}y+\cfrac{2}{9} \right)=360\left( \cfrac{5}{8}-\cfrac{2}{5}y+\cfrac{5}{8} \right)} \\\\\\ 72(3y)+40(2)=45(5)-72(2y)+45(5) \\\\\\ 216y+80=225-144y+225\implies 216y+80=450-144y \\\\\\ 216y=370-144y\implies 360y=370\implies y=\cfrac{370}{360}\implies y=\cfrac{37}{36}[/tex]

Answer:

B. g(x) = |x + 3|

Step-by-step explanation:

Answer:

[tex]3m =\frac{57}{5}=11.4=11\ \frac{2}{5}[/tex]

Step-by-step explanation:

We know that

[tex]m = 3\ \frac{4}{5}[/tex]

Therefore

[tex]m = 3+\frac{4}{5}\\\\m=\frac{19}{5}[/tex]

Now multiply the value of m by 3.

[tex]m=\frac{19}{5}\\\\3m=3*\frac{19}{5}\\\\3m =\frac{57}{5}=11.4[/tex]

The answer is 3m = 11.4

ANSWER

C. 33 units^2

EXPLANATION

The area of a kite is half times product of the diagonals.

The diagonals are

3+3=6 units

and

9+2 =11 units.

The area of the kite is

[tex] = \frac{1}{2} \times 11 \times 6[/tex]

[tex] = 11 \times 3[/tex]

[tex] = 33 {units}^{2} [/tex]

The correct choice is C

To calculate the likelihood of drawing cards 5 and 6 in sequence from a shuffled deck of 8 cards, we multiply the individual probabilities of drawing each card. The result is a probability of 1/56.

The question asked is a probability question which involves finding the likelihood of drawing two specific cards in sequence from a shuffled deck. However, the detailed information provided relates to different scenarios involving card colors numbered cards, and rolling dice. It does not directly provide the information needed for calculating the specific probability of selecting cards 5 and 6 from a stack of 8 cards numbered 1-8. Nonetheless, if we base our calculation on a standard probabilistic approach without considering the provided scenarios:

The probability of selecting the card number 5 first from the stack of 8 is 1/8 since there is one card number 5 out of eight total cards. Once card number 5 has been selected, it is no longer in the stack, so there are now seven cards left. The probability of selecting card number 6 after that is 1/7. Therefore, the probability of selecting card 5 and then card 6 in the sequence is the product of the two probabilities: 1/8 * 1/7 = 1/56.

Answer:

The answer is 195

Step-by-step explanation:

The formula is V= 1/2 of the height times the two bases

V=1/2*h*b*b

V=1/2*13*6*5

V=195 meters squared.

Hoped this helped!

Answer: 390

Step-by-step explanation:

Length x Width x Height = Volume

17k−25 is the answer.

Expressions are equal if they may be simplified to the same 0.33 expression or if one of the expressions can be written just like the other. similarly, you can additionally determine if two expressions are equal when values are substituted in for the variable and both arrive at an equal solution.

Algebraic expressions are equal in the event that they constantly lead to the same result whilst you evaluate them, irrespective of what values you substitute for the variables. For instance, if x = three, then x + x + 4 = three + three + 4 = 10 and 2x + 4 = 2(3) + four = 10 additionally.

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The value of F in terms of K is (9K - 2298.67)/5.

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Here, given function:

                     K = 5/9 (F + 459.67)

                   9K = 5(F + 459.67)

                   9K = 5F + 2298.67

                   9K - 2298.67 = 5F

                   F =(9K - 2298.67)/5

Thus, the value of F in terms of K is (9K - 2298.67)/5.

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To solve for F in terms of K, you can use the equation F = (9/5)(K) - 459.67.

To solve for F in terms of K, we need to isolate F on one side of the equation.

Step 1: Start with the given equation:

K = (5/9)(F + 459.67)

Step 2: Multiply both sides of the equation by 9/5 to undo the multiplication on the right side:

(9/5)(K) = F + 459.67

Step 3: Simplify the left side:

(9/5)(K) = F + 459.67

Step 4: Subtract 459.67 from both sides to isolate F:

(9/5)(K) - 459.67 = F

Therefore, F in terms of K is given by the equation F = (9/5)(K) - 459.67.

6(7-4)+10

First distribute 6 into the parentheses

42-24+10= 28

So your answer is A. 28

Final answer:

To evaluate 6(x - 4) + 10 when x = 7, after substituting and simplifying, the result is 28 (option A).

Explanation:

Step-by-Step Solution

To evaluate the expression 6(x - 4) + 10 when x = 7, follow these steps:

Therefore, the expression 6(x - 4) + 10 when x = 7 equals to option A. 28.

Answer:

[tex]AC=\frac{11\sqrt{3}}{3}[/tex]

Step-by-step explanation:

Given that triangle ABC is a right angle triangle. Where angle C is a right angle. Also we have been given that BC = 11, B = 30°. Now we need to find the value of AC.

Apply formula:

[tex]\tan\left(\theta\right)=\frac{opposite}{adjacent}[/tex]

[tex]\tan\left(B\right)=\frac{AC}{BC}[/tex]

[tex]\tan\left(30^o\right)=\frac{AC}{11}[/tex]

[tex]\frac{1}{\sqrt{3}}=\frac{AC}{11}[/tex]

[tex]\frac{11}{\sqrt{3}}=AC[/tex]

[tex]AC=\frac{11}{\sqrt{3}}[/tex]

or

[tex]AC=\frac{11}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}[/tex]

or

[tex]AC=\frac{11\sqrt{3}}{3}[/tex]

Hence final answer is [tex]AC=\frac{11\sqrt{3}}{3}[/tex].

Answer:

D. [tex]g(x)=-2^x[/tex]

Step-by-step explanation:

We can use a process of elimination in order to easily solve this.

The shape of [tex]g(x)=-|x|[/tex] will be two diagonal lines that meet at (0,0)

[tex]g(x)=-x^2[/tex] Will be an upside down parabola

[tex]g(x)=-x[/tex] Will be a line with a slope of -1.

This means that the answer must be D

Answer:

The correct option is D.

Step-by-step explanation:

From the given graph it is clear that the y-intercept of the function is -1. It means the graph passes through (0,-1).

Check each function, whether the function passes through the point (0,-1) or not. Substitute x=0 it each function to find the y-intercept.

In option A,

[tex]g(x)=|x|[/tex]

[tex]g(0)=|0|=0[/tex]

The y-intercept of the function is at (0,0).

In option B,

[tex]g(x)=x^2[/tex]

[tex]g(0)=0^2=0[/tex]

The y-intercept of the function is at (0,0).

In option C,

[tex]g(x)=x[/tex]

[tex]g(0)=0[/tex]

The y-intercept of the function is at (0,0).

In option D,

[tex]g(x)=-2^x[/tex]

[tex]g(0)=-1[/tex]

The y-intercept of the function is at (0,-1).

The graph of [tex]g(x)=-2^x[/tex] passes through the point (0,-1).

Therefore the correct option is D.

Answer:

120 cm^3

Step-by-step explanation:

volume = lwh

I = 4 centimeters  

w = 5 centimeters  

h = 6 centimeters

volume = (4 cm)(5 cm)(6 cm)

volume = 120 cm^3

Answer:

I'm pretty sure it's the one you chose, which means the 2nd pic.

Answer:

I think It is the first one, that is a cone flipped and there is a hole in it.

x+5/30 = 50/75

x+5/10 = 2

x+5 = 20

x = 15

Answer

1) [tex]b=101\degree[/tex]

2) [tex]m=50\degree[/tex]

3) [tex]h=79\degree[/tex]

4) [tex]g=101\degree[/tex]

5) [tex]i=51\degree[/tex]

6) [tex]j=130\degree[/tex]

Explanation

From the diagram,

[tex]b=101\degree[/tex], corresponding angles are equal.

From the diagram, m=k, corresponding angles are equal.

But k+130=180, angles on a straight line sum up to 180 degrees.

This implies that k=180-130=50

[tex]\therefore m=50\degree[/tex]

From the diagram ; [tex]h+101=180\degree[/tex],angles on a straight line sum up to 180 degrees.

[tex]\implies h=180-101\degree[/tex]

[tex]\implies h=79\degree[/tex]

From the diagram, [tex]g=101\degree[/tex] vertically opposite angles are equal.

From the triangular portion;

i+h+m=180. sum of interior angles of a triangle.

This implies that:

i+79+50=180

i+129=180

i=180-129

[tex]i=51\degree[/tex]

Finally

[tex]j=130\degree[/tex], vertically opposite angles are equal.

Answer:

Part 1) ∠b=101°

Part 2) ∠m=50°

Part 3) ∠h=79°

Part 4) ∠g=101°

Part 5) ∠i=51°

Part 6) ∠j=130°

Step-by-step explanation:

Part 1) ∠b

we know that

∠b=101° ------> by corresponding angles

Part 2) ∠m

we know that

∠m=∠k ------> by corresponding angles

and

∠k+130°=180° -----> by supplementary angles

∠k=180°-130°=50°

therefore

∠m=50°

Part 3) ∠h

we know that

∠h+101°=180° -----> by supplementary angles

∠h=180°-101°=79°

Part 4) ∠g

we know that

∠g=101° -----> by vertical angles

Part 5) ∠i

we know that

The sum of internal angles of a triangle must be equal to 180 degrees

so

∠h+∠m+∠i=180°

substitute the values and solve for ∠i

79°+50°+∠i=180°

∠i=180°-129°=51°

Part 6) ∠j

we know that

∠j=130° -----> by vertical angles

Answer:

48984 m^2

Step-by-step explanation:

The height(h) of cone is given by: 50 m.

Diameter of cone is: 240 m.

Also radius(r) of cone is:240/2=120 m.

The lateral surface(S) area is given by:

The lateral area of the cone comes out to be 48984 m^2.

What is lateral area?

The formula of the lateral area of cone is given by, area = pi×r×L

The amount of territory occupied by the curved surface area of a cone is known as the lateral surface area.

The lateral surface area of a cone is also in the three-dimensional plane because it is a three-dimensional form. The shape of a cone is created by stacking and rotating several triangles around an axis. Since a cone has a flat base so it has curved surafce area as well as total surface area.  A cone's lateral area is measured in square units, such as cm2, m2, in2, and so on.

Given,

Height of cone : 50m

Diameter of cone: 240m

so,it's radius will be 120m

L = [tex]\sqrt{r^{2}+h^{2}}[/tex]

L = [tex]\sqrt{120^{2} +50^{2} }[/tex]

L = 130

since,Area = pi×r×L

=3.14×120×130

=48984m^2

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Answer:

80

Step-by-step explanation:

Answer:

D. (2, 6)

Step-by-step explanation:

Look at the picture.

Check:

(2, 6) → x = 2, y = 6

Put the coordinates of the point to the inequalities:

y < x² + 6

6 < 2² + 6

6 < 4 + 6

6 < 10    TRUE

y > x² - 4

6 > 2² - 4

6 > 4 - 4

6 > 0   TRUE

Final answer:

The correct solution to the system of inequalities is point D (2,6), as it satisfies both inequalities y < x^2 +6 and y > x^2 -4 when x=2 and y=6 are substituted into them.

Explanation:

The student is asked to select the point that is a solution to the system of inequalities.

The two inequalities given are:

< x^2 +6

y > x^2 -4

To solve this, we need to check which point(s) satisfy both inequalities. Let's evaluate the options given:

A. (0,8): Substituting x=0 into both inequalities gives 8 < 6 (false) and 8 > -4 (true), so point A does not satisfy both inequalities.

B. (-2,-4): Substituting x=-2 into both inequalities gives -4 < 10 (true) and -4 > 0 (false), so point B does not satisfy both inequalities.

C. (4,2): Substituting x=4 into both inequalities gives 2 < 22 (true) and 2 > 12 (false), so point C does not satisfy both inequalities.

D. (2,6): Substituting x=2 into both inequalities gives 6 < 10 (true) and 6 > 0 (true), so point D satisfies both inequalities and is the correct solution.

Therefore, the solution to the system of inequalities is point D (2,6).

Answer:

$4,723.21​

Step-by-step explanation:

Formula for COMPOUND INTEREST:

A = P ( 1 + r/n) ^ nt

Where A = principal money + interest earned,

P = Principal Money

r = interest rate in decmial

n = no. of times i.rate is compounded

nt = time

Since the qns asked to be compounded /monthly', you have the following formula:

A = 3250 ( 1 + 7.5%/12) ^ 60

7.5% is a yearly rate so divide it by 12 (as in 12 months)

60 = 5 years x 12 months

so use a calculator and you'll get $4723.206, round off and it's $4723.21

To find out how much Connie's investment in a savings account with a 7.5% annual interest rate compounded monthly will be worth in five years, use the compound interest formula. After calculations, her investment will be worth $4,723.21 in five years.

The student asks about the future value of an investment made in a savings account with compound interest. To calculate the amount Connie's investment will be worth in five years, we can use the compound interest formula, which is A = P(1 + r/n)^(nt). Here, P is the principal amount ($3,250), r is the annual interest rate (7.5% or 0.075 as a decimal), n is the number of times the interest is compounded per year (12, since it's monthly), and t is the number of years (5).

Using these values, we calculate the future value (A) as follows:

Convert the percent interest to a decimal: 7.5% = 0.075.

Divide the annual rate by the number of compounding periods: 0.075/12.

Add 1 to the interest rate per period: 1 + (0.075/12).

Calculate (1 + (0.075/12)) raised to the power of the total number of compounding periods: (1 + (0.075/12))^(12*5).

Multiply the principal by this amount: $3,250 × (1 + (0.075/12))^(12*5).

Connie's investment will grow to $$4,723.21 after five years, using compound interest.

Answer:

128

Step-by-step explanation:

To create 128 different hamburgers with multiple combinations of condiments, you would need 7 different condiments. This is due to the fact that each condiment presents 2 possibilities, on the burger or not, and 2 to the power of 7 equals 128.

In this scenario, each condiment represents an option that can be either included or excluded. This means that, for each condiment, there are 2 possibilities (it's either on the burger, or it's not). The question implies that the number of possible combinations equals 128, which is 2 to the power of 7.

So, to create 128 different hamburgers, the restaurant must offer 7 different condiments. This is because 2 (possibilities for each condiment) to the power of 7 (condiments) equals 128.

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Answer:

a)zw  = 44.295 cos(1.924) +isin(1.924))

b) z/w= 4.921 cos(-0.936) + isin(-0.936)

Step-by-step explanation:

Given:

z=13+7i

w=3(cos(1.43)+isin(1.43)  

a. convert zw using De Moivre's theorem  

First coverting z into  polar form:

13^2 + 7^2  = 14.765

[tex]\sqrt{14.765}[/tex] =r

θ= arctan (7/13)

 = 0.49394                            (28.301 in degrees)

z= 14.765(cos(0.49394)+isin(0.49394)  )

Now finding zw

zw= 14.765(cos(.494)+isin(.494))×3(cos(1.43)+isin(1.43))

Using De Moivre's theorem, the modulus will be multiplied

14.765 x 3=44.295

whereas the angles will be added

.494+1.43=1.924

Thus:

zw  = 44.295 cos(1.924) +isin(1.924))

b)

finding z/w

z/w= 14.765(cos(.494)+isin(.494)) / 3(cos(1.43)+isin(1.43))

Using De Moivre's theorem, the modulus will be divided

14.765 / 3 = 4.921

whereas the angles will be subtracted:

.494-1.43=-0.936

Thus:

z/w= 4.921 cos(-0.936) + isin(-0.936) !

Answer:

Step-by-step explanation:

The sample space should show all the possible outcomes.

The first option includes all 4 colors and both head and tails.

The second option is missing tails as an outcome.

The third option is missing blue.

The fourth option is missing tails.

So it must be the first one.

Answer:

The number of cutters is 7

The number of screw drivers is 22

Step-by-step explanation:

Let

x-----> the number of cutters

y----> the number of screw drivers

we know that

x+y=29 ----> equation A

15.2x+2y=150.40 ----> equation B

Solve the system of equations by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The solution is the point (7,22)

see the attached figure

therefore

The number of cutters is 7

The number of screw drivers is 22

The width of the border around the stained glass window is approximately 1.15 feet, calculated by subtracting the stained glass area from the total area including the border.

To find the width of the border, we need to subtract the area of the stained glass window from the total area including the border.

Given:

- Length of stained glass window = 4 feet

- Width of stained glass window = 2 feet

- Area of stained glass window = [tex]\(4 \times 2 = 8\)[/tex] square feet

- Total area including the border = Area of stained glass window + Area of border = 8 + 7 = 15 square feet

Let's denote the width of the border as x feet.

The total length including the border is 4 + 2x feet, and the total width including the border is 2 + 2x feet.

The area of the total window with the border is the product of its length and width:

(4 + 2x)(2 + 2x) = 15

Expanding this equation:

8 + 4x + 4x + 4x^2 = 15

8 + 8x + 4x^2 = 15

4x^2 + 8x - 7 = 0

Now, let's solve this quadratic equation using the quadratic formula:

[tex]\[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}\][/tex]

Where a = 4, b = 8, and c = -7.

[tex]\[x = \frac{{-8 \pm \sqrt{{8^2 - 4 \times 4 \times (-7)}}}}{{2 \times 4}}\][/tex]

[tex]\[x = \frac{{-8 \pm \sqrt{{64 + 112}}}}{8}\][/tex]

[tex]\[x = \frac{{-8 \pm \sqrt{{176}}}}{8}\][/tex]

[tex]\[x = \frac{{-8 \pm 4\sqrt{{11}}}}{8}\][/tex]

[tex]\[x = \frac{{-2 \pm \sqrt{{11}}}}{2}\][/tex]

Since the width cannot be negative, we take the positive root:

[tex]\[x = \frac{{-2 + \sqrt{{11}}}}{2} \approx 1.15 \text{ feet}\][/tex]

Therefore, the width of the border is approximately 1.15 feet.