1. Nina had Marbles. She gave 15 to Jane and 16 to Cherry. Louie arrived and got 12 from Nina. If Nina has 22 left, how many marbles did she have at first?

The distance between the two ship based on the angle of depression is 42 meters.

The distance of each ship can be calculated thus:

TanX = opposite / Adjacent

The first ship:

Tan53 = distance/ 82

distance= 108.82 meters

The second ship:

Tan39 = distance/ 82

distance= 66.40 meters

The Difference between the ships are :

Therefore, the distance between the two ships is 42 meters.

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I provided tape diagram in attachment

The amount of money in the account after 18 years will be $449.5.  

Given is that every Morning, Julio drives his 1.5 hour route to gather the children for school. His route covers 45 miles and there are 60 kids on the route.

Refer to the tape diagram given. It shows that in one hour, a total of 30 miles have been covered.

Therefore, the amount of money in the account after 18 years will be $449.5.  

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You have a 5% chance of being wrong with a 95% confidence interval. With a 90 percent certainty span, you have a 10 percent chance of being incorrectly.

A confidence interval of ninety-nine percent would be larger than a confidence interval of ninety-five percent (for instance, plus or minus 4.5 percent as opposed to 3.5 percent).

We now have: 32 125 0.256 1 At a confidence level of 95 percent:

Zenit = 20.05/2 = 2196 95 percent confidence interval:

Considering the estimated proportion (P) = 0.256 n = = Zverit PL1-P) E 1.96 12 0.015) 0.256 (1-0.256) = 3251.94 3252

Zerit = 20.05/2 = 1.96 At 95%

confidence lovel margin of error (E) = 0.015

Now P = zerit / PL1-£) = 0.256  1.96 X 0.2561-0.256 125 = 0.256  0.0765.

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what is the equation in slope- intercept form of the line that passes through the points (-26 -11) and (39, 34) ?



A) y = -9/13 x + 7

B) y = -9/13 x - 7

C) y = 9/13 x + 7

D) y = 9/13 x - 7 ​

step 1

Find out the slope

m=(34+11)/(39+26)

m=45/65

simplify

m=9/13

step 2

Find the equation in slope intercept form

y=mx+b

we have

m=9/13

point (39,34)

substitute and solve for b

34=(9/13)(39)+b

b=34-27

b=7

therefore

the equation is

y=(9/13)x+7

Answer:

A.  (x - 80)² = -320(y = 20)

B.  Focus:  (80, -60)

     Directrix:  y = 100

     Axis of symmetry:  x = 80

Step-by-step explanation:

If the spider's movement is modeled by a parabola, and its maximum height is 20 mm halfway across a horizontal distance of 160 mm, then:

Standard form of a parabola with a vertical axis of symmetry:

\(\boxed{(x-h)^2=4p(y-k) \quad \textsf{where}\:p\neq 0}\)

If p > 0, the parabola opens upwards, and if p < 0, the parabola opens downwards.

Substitute one of the x-intercepts and the vertex into the formula and solve for p:

\(\implies (0-80)^2=4p(0-20)\)

\(\implies (-80)^2=4p(-20)\)

\(\implies 6400=-80p\)

\(\implies p=-80\)

Substitute the found value of p and the vertex into the formula to create the equation of the parabola in standard form:

\(\implies (x-80)^2=4(-80)(y-20)\)

\(\implies (x-80)^2=-320(y-20)\)

Given:

\(\begin{aligned}\textsf{Focus}&=(h,k+p)\\&=(80,20-80)\\&=(80,-60)\end{aligned}\)

\(\begin{aligned}\textsf{Directrix}:y&=(k-p)\\ \implies y&=(20-(-80))\\ \implies y&=100\end{aligned}\)

\(\begin{aligned}\textsf{Axis of symmetry}:x&=h\\ \implies x&=80\end{aligned}\)

Using it's concept, the range of the relation is given by:

{0, 1, 3, 6, 11}.

The range of a relation is the set that contains all output values of the relation, that is, all values of y.

The points given are in the (x,y) format, hence the range of the relation is given by:

{0, 1, 3, 6, 11}.

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Answer:

Kindly refer to the attachment

Answer:

52

Step-by-step explanation:

RTQ is 52 because if PTR is a right angle, right angles equal 90 degrees. So if PTQ is 38 degrees, we subtract 38 from 90 to get RTQ. 90-38 equals 52.

Answer:

52 degrees

Step-by-step explanation:

right angle = 90

90-38=52

So RTQ = 52 degrees

Answer:

Step-by-step explanation:

a) If a driver uses a full tank of gas every day, the fraction of a tank he will use in 3 days is 3/1, or 3/1 of a tank.

b) If a driver uses a full tank of gas every day, the fraction of a tank he will use in 1 week is 7/1, or 7/1 of a tank.

It's worth noting that tanks of gas come in different sizes, so the amount of gas consumed in a day, week, or any other period of time will depend on the size of the tank, and the consumption of the car, so this answer is based on the assumption that a full tank is used every day.

Answer: We can solve this problem by finding the total weight of the meat and then dividing by the weight of each patty to see if we can make the desired number of patties.

Let's add the weights of the two packages of meat:

10 + 11.5 = 21.5

For option A, we need 87 1/4-pound patties.

Each pound of meat will yield 4 patties of this size, so 21.5 pounds of meat will yield:

21.5 x 4 = 86 patties

Since we need 87 patties, Claude does not have enough meat for option A.

For option B, we need 45 1/2-pound patties.

Each pound of meat will yield 2 patties of this size, so 21.5 pounds of meat will yield:

21.5 x 2 = 43 patties

Since we need 45 patties, Claude does not have enough meat for option B.

For option C, we need 30 1/2-pound patties and 2 74-pound patties.

Each pound of meat will yield 2 patties of the smaller size and 1 patty of the larger size, so 21.5 pounds of meat will yield:

(21.5 x 2) + (2 x 1) = 43 + 2 = 45 patties

Since Claude only has 21.5 pounds of meat, he does not have enough for option C.

For option D, we need 29 3/4-pound patties.

Each pound of meat will yield 1.5 patties of this size, so 21.5 pounds of meat will yield:

21.5 x 1.5 = 32.25 patties

Since we only need 29.75 patties, Claude has enough meat for option D.

Therefore, the answer is Yes, Claude can make 29 3/4-pound hamburger patties.

answer

-z•1=-3-1

z=-3•-1

z=3

The midpoint of the line segment with endpoints (2, 6) and (10, 4) is (6, 5).

To find the midpoint of a line segment, we can use the midpoint formula, which states that the coordinates of the midpoint are the average of the coordinates of the endpoints.

Let's denote the coordinates of the first endpoint as (x1, y1) and the coordinates of the second endpoint as (x2, y2).

In this case, the first endpoint is (2, 6) with coordinates (x1, y1) = (2, 6), and the second endpoint is (10, 4) with coordinates (x2, y2) = (10, 4).

To find the midpoint, we use the midpoint formula:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Plugging in the values, we have:

Midpoint = ((2 + 10) / 2, (6 + 4) / 2)

= (12 / 2, 10 / 2)

= (6, 5)

As a result, (6, 5) is the point on the line segment where the endpoints are (2, 6) and (10, 4) respectively.

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Answer:

А Yes

Step-by-step explanation:

Graphic solutions of inequalities:

Generally, if the point is a painted region, it is a solution of the inequality, while if it is in a non-painted region, it is not a solution.

Is (0,-5) a solution of the graphed system of inequalities?

Point (0,-5) is 0 on the x-axis and -5 on the y-axis, which is painted, on the bottom part of the graphic, so it is a solutiom of the graphed system, and the correct answer is given by option A.

Using DeMoivre’s theorem, the answer in regular form would be (5 + 5√3i)⁷ = -5000000 + 8660254.03i

The De Moivre's Theorem is used to simplify the computation of powers and roots of complex numbers and is used in together with polar form.

Convert the complex number to polar form. The polar form of a complex number is z = r(cos θ + isin θ),

r = |z|  magnitude of z

it becomes

r = √((5)² + (5√3)²) = 10

θ = arg(z) is the argument of z.

θ = atan2(b, a) = atan2(5√3, 5) = π/3

(5 + 5√3i) = 10 × (cos π/3 + i sin π/3)

De Moivre's theorem to raise the complex number to the 7th power

(5 + 5√3i)⁷

= 10⁷× (cos 7π/3 + i sin 7π/3)

= 10⁷ × (cos 2π/3 + i sin 2π/3)

Convert this back to rectangular form:

Real part = r cos θ = 10⁷× cos (2π/3) = -5000000

Imaginary part = r sin θ = 10⁷ × sin (2π/3) = 5000000√3 = 8660254.03i

∴  (5 + 5√3i)⁷ = -5000000 + 8660254.03i

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Answer:10^7 (1/2 - √3/2 i)

Step-by-step explanation:

To use DeMoivre's theorem, we first need to write the number in polar form. Let's find the magnitude and argument of the number:

Magnitude:

|5 + 5√(3i)| = √(5^2 + (5√3)^2) = √(25 + 75) = √100 = 10

Argument:

arg(5 + 5√(3i)) = tan^(-1)(√3) = π/3

So the number can be written in polar form as:

5 + 5√(3i) = 10(cos(π/3) + i sin(π/3))

Now we can use DeMoivre's theorem:

(5 + 5√(3i))^7 = 10^7 (cos(7π/3) + i sin(7π/3))

To simplify, we need to find the cosine and sine of 7π/3:

cos(7π/3) = cos(π/3) = 1/2

sin(7π/3) = -sin(π/3) = -√3/2

Explanation:

So the final answer in rectangular form is:

10^7 (1/2 - √3/2 i)

\(W = 23.7°\)

Step-by-step explanation:

The formula given is the statement of Snell's law of refraction. We are given the following:

\(I_a = 1.0003\)

\(I_w = 1.3\)

\(A = 31.5°\)

So we need to find the angle of refraction W. Starting with Snell's law,

\(\dfrac{I_w}{I_a} = \dfrac{\sin A}{\sin W} \Rightarrow \sin W = \left(\dfrac{I_a}{I_w}\right)\sin A\)

Plugging in the given values, we get

\(\sin W = \left(\dfrac{1.0003}{1.3}\right)\sin{31.5°} = 0.402\)

Solving for the angle W, we then get

\(W = \sin^{-1}(0.402) = 23.7°\)

The rectangular form of the polar expression \(12(cos\pi+ isin\pi)\) is -12

The given equation is:

\(12(cos\pi+ isin\pi)\)

The above equation is in polar form

Note that:

\(cos \pi = -1\\\\sin\pi = 0\)

Substituting \(cos \pi = -1\) and \(sin \pi = 0\) into the expression \(12(cos\pi+ isin\pi)\) in order to get the rectangular form of the expression

\(12(cos\pi+ isin\pi)\)

=  12(-1   +   1(0))

=  12 ( -1  +  0)

=  12(-1)

=  -12

Therefore, the rectangular form of the polar expression \(12(cos\pi+ isin\pi)\) is -12

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Answer:

SAS

Step-by-step explanation:

The required coordinate of B' is B' = (4, -5), across the y-axis after reflection. Option A is correct.

Transform the shapes on a coordinate plane by rotating, reflecting, or translating them.

here,
Given that a point B (-4, -5) is reflected across the y-axis, the Coordinate of image B' is to be determined.

Since the coordinate is reflected across the y-axis,
The equation of trasformation is given as,
(x , y) ⇒ (-x , y)

So, the image of B,

B' = (-(-4), -5)

B' = (4, -5)

Thus, the required coordinate of B' is B' = (4, -5), across the y-axis after reflection. Option A is correct.

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Answer:

1.93g/cm^3 = density

Step-by-step explanation:

M = p • v

M = mass

p = density

v = volume

volume = l • w • h

volume = 10.0 cm • 2.0 cm • 5.0 cm

volume = 100 cm^3

193.0g = p • 100cm^3

divide each side by 100cm^3

1.93g/cm^3 = p

The best way to solve an equation of the form Ax+by=c could be either substitution, completing the squares or graphical method depending on the type of equation given.

Quadratic equation

The equation in the form Ax+by=c is a quadratic problem which could be approached in different ways depending on the specific equation given and the information provided.

The methods of approach are substitution, completing the squares or graphical method which all have proven to be suitable ways to arrive at the solution.

Hence, either of the three methods are good ways to solve such equation.

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Answer:

C

Step-by-step explanation:

P-25

Answer:

59.96

Step-by-step explanation:

when 67% if 89.5 is expressed in numbers,

\(\frac{67}{100}*89.5\\ \frac{5996.5}{100}\\ =59.96\)

Answer:

It is better to buy the 16-ounce drink and it is 0.01 cent cheaper

Step-by-step explanation:

We have to find out how much each sports drinks cost per ounce.

0.96 ÷ 12 = 0.08 per ounce

1.12 ÷ 16 = 0.07 per ounce

It is better to buy the 16-ounce drink and it is 0.01 cent cheaper

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Answer: 2.214285714, probably B maybe? I'm not sure what D is.

Step-by-step explanation: (14)x + 1 = 32.

Your goal here is to get the x by itself so that you will know how much it is worth.

First step I would take is to subtract 1 from both sides to get rid of the one on the side with the x. What you do on one side is what you must do on the other side.

Now you have (14)x = 31

Next step I would take is divide both sides by 14 so that you can finally get the x by itself.

Now you have 2.214285714, so I would choose whatever answer that is closest to.

Answer:

d)  28 in²

Step-by-step explanation:

A = bh

A = 7h

Find 'h' by using the Pythagorean Theorem:

3² + h² = 5²

9 + h² = 25

h² = 16

h = √16 = 4

A = 7×4 = 28

Answer:28

Step-by-step explanation:

Area of a parallelogram= bh

base-7

height- 4

using the Pythagorean theorem, \(5^{2}\) - \(3^{2}\)= \(\sqrt{16}\) = 4

7 * 4 = 28

Answer:

65

Step-by-step explanation:

The lines are parallell so m1 = m5, and m3=m8. 180-115 is 65

Answer:

It is possible to draw a triangle with the given side lengths of 11, 10, and 20 because the sum of any two side lengths is greater than the length of the 3rd side as stated in the Triangle Inequality Theorem.

Explanation:

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

So given the side lengths of 11, 10, and 20, let's see if it satisfies the above conditions;

We can see from the above that the condition in the above theorem is satisfied, therefore, we can say that it is possible to draw a triangle with the given side lengths of 11, 10, and 20.