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Final answer:

To find sin 2θ when cos θ = 3/5, we first find sin θ using the Pythagorean identity and then apply the double angle formula, yielding sin 2θ = 24/25.

Explanation:

To find sin 2θ when given cos θ = 3/5 and θ is in the first quadrant, we can use the double angle formula for sine, which is sin 2θ = 2 sin θ cos θ. First, we need to find sin θ. Given that θ is in the first quadrant, all trigonometric functions are positive, and we can use the Pythagorean identity sin²θ + cos²θ = 1 to find sin θ. Since we know cos θ, cos²θ = (3/5)² = 9/25, which means sin²θ = 1 - 9/25 = 16/25. Taking the positive square root, since θ is in the first quadrant, sin θ = 4/5.

Now, we apply the double angle formula: sin 2θ = 2 × (4/5) × (3/5), which simplifies to sin 2θ = 24/25.

Answer:

A

Step-by-step explanation:

If we take each small section to be "1" unit, we can say the large sections (for "2" and "5") are "2" units each. So in total there will be 8 sections.

Since 5 is "2" sections, we can say:

P(5) = 2/8 = 1/4

And 6 is "1" section, so we can say:

P(6) = 1/8

Definitely, Probability of landing a 6 is HALF that of probability of landing a 5. Also we can see this is the picture.

So, from the answer choices, A is right.

Answer:

160 ounces

Step-by-step explanation:

1 pound=16 ounces

so,

10 pounds=16 multiplied by 10= 160 ounces

Fun fact u spelled ounces at the very last.

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The weight of the 10-pound package is 160 ounces.

There are 16 ounces in 1 pound. Juan is mailing a packet that weighs 10 pounds. To find the weight of the package in ounces, multiply the number of pounds (10) by the unit equivalence (16).

Therefore, the weight of the package is 160 ounces.

Answer:

b)−1×2×−3×4×−5 has a negative value.

Step-by-step explanation:

Given expressions are a)−1×−2  b)−1×2×−3×4×−5 C) 1×−2×−3×−4×−5 d)1×−2×3×−4×5

Firstly we have to multiply the digits with digit then after minus sign.

So for a)−1×−2

Solution, [tex]1\times2\ =2[/tex]

When two negative signs are multiplied with each other it gives a positive sign.

Both digits have a negative sign that means it gives a positive sign.

So the solution for 1st expression is [tex]2.[/tex]

b)−1×2×−3×4×−5

Solution,[tex]1\times2\times3\times4\times5\ =120[/tex]

Here three digits have negative sign, two negative gives positive and then multiplied by negative gives negative.

So the solution for 2nd expression is [tex]-120[/tex].

C) 1×−2×−3×−4×−5

Solution,[tex]1\times2\times3\times4\times5\ =120[/tex]

Here four digits have negative sign, two negative gives positive and again two negative gives positive means positive multiplied with positive gives positive.

So the solution for 3rd expression is [tex]120[/tex].

d)1×−2×3×−4×5

Solution,[tex]1\times2\times3\times4\times5\ =120[/tex]

Two digits have a negative sign that means it gives a positive sign.

So the solution for 4th expression is [tex]120[/tex].

Hence the correct option is b.

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

9/16=x/12

cross product

16x=9*12

16x=108

x=108/16

simplify

x=27/4

---------------

x-3/18=12/9

x=12/9+3/18

x=24/18+3/18

x=27/18

x=3/2

--------------------

7/11=18/x+1

18/x=7/11-1

18/x=7/11-11/11

18/x=-4/11

x=18/(-4/11)=(18/1)(-11/4)=-198/4=-99/2

x=-99/2

The total number of nails will decrease by 14 nails when Willa will use 7 nails on each side.

Step-by-step explanation:

Sides of one birdhouse = 7

Nails used on each side = 9

Nails used on one birdhouse = Nails per side * Sides of birdhouse

Nails used on one birdhouse = 9*7 = 63 nails

If she uses 7 nails on each side, then the number of nails used on one birdhouse;

No. of nails = 7 * 7 = 49 nails

Change = Nails used on one birdhouse - No. of nails

Change = 63 - 49 = 14

The total number of nails will decrease by 14 nails when Willa will use 7 nails on each side.

Keywords: multiplication, subtraction

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Each birdhouse needs 63 nails. If Willa uses only 7 nails on each side, she will need a total of 49 nails.

Each side of the birdhouse requires 9 nails, and there are 7 sides on the birdhouse. To find the total number of nails needed for each birdhouse, we can multiply the number of nails per side by the number of sides:

9 nails/side x 7 sides = 63 nails needed for each birdhouse.

If Willa only uses 7 nails on each side, the total number of nails she uses will change. The new total number of nails can be found by multiplying the new number of nails per side (7 nails) by the number of sides (7 sides):

7 nails/side x 7 sides = 49 nails in total.

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Answer:

96 is the answer maybe of it

Answer:

11

Step-by-step explanation:

because that are 11 pencils that are 6 inches or longer, that's what the picture says.

Answer:

Helpful piece of information - each x = 1 pencil

Step-by-step explanation:

If each x = 1 pencil, and their are 6 x's over the 6 inch mark, 2 x's over the 7 inch mark, and 3 x's over the 8 inch mark, how many pencils measure 6 inches or more?

11 pencils measure 6, 7, and 8 inches.

I hope this helps!

Answer:

about 160

Step-by-step explanation:

Answer:

1440 CUVs, approx.  Actual number would be slightly lower.

Step-by-step explanation:

To answer this question, multiply 4800 vehicles by (3/10) for an approximation of the number of CUVs sold:

4800        3

---------- * ------- = 1440 CUVs

    1            10

Answer:

[tex]x=-\frac{88}{3}[/tex]

Step-by-step explanation:

When a quantity "A" varies DIRECTLY with another quantity "B", we can write the proportionality equation as:

A = kB

Where k is the proportionality constant (to be found)

In this problem, it is given x varies DIRECTLY with y, so we can write:

x = ky

Also, given, x = 11, y = -3, so we plug these into the equation and first find k:

x = ky

11 = k(-3)

k = -11/3

Now, we need to find x when y = 8, so we substitute and find x:

[tex]x=ky\\x=(-\frac{11}{3})(8)\\x=-\frac{88}{3}[/tex]

To find x for a given value of y when x varies directly as y, determine the constant of proportionality using the provided pair of values. Then use this constant to calculate x for the new value of y.

Since x varies directly as y, we can write this as x = ky, where k is the constant of proportionality. To find the value of k, we use the given values: x=11 when y=-3. Substituting these values into the equation gives us 11 = k(-3), or k = -11/3.

To find x when y=8, we substitute y=8 and the value of k into the direct variation equation: x = (-11/3)(8) = -88/3 = -29.33. Therefore, x is approximately -29.33 when y=8.

Answer:

Original point (1,2) and the image is (1,-2).

Step-by-step explanation:

If a point on the coordinate plane reflects across the x-axis then the x-coordinates of the original point and that of the image point will remain the same and the y-coordinates of the original point and that of the image point will only change their signs.

So, a point having coordinates (a,b) when reflected across the x-axis then the point generated after reflection will have coordinates (a,-b).

This is true for any real values of a and b.

So, for example, if (1,2) is a point reflected across the x-axis will generate an image point with coordinates (1,-2). (Answer)

Rounding to the greatest place value requires focusing on the digit to the right of the place value you're rounding to. If it's 5 or above, round up, if less, round down. This makes calculations easier by providing an estimated value close to the actual one.

In this question, you are asked to estimate a value by rounding to the greatest place value. To do this, you will focus on the digit in the place value you are rounding to and the digit to its right. If the digit is 5 or more, you will round up. If it's less than 5, you will round down. It's called the estimation because it's not an exact value but a value close to the actual one best suited for calculations.

For example, if you have the number 4387 and you want to round it to the greatest place value, which is thousands place, you will look at the hundreds place value which is 8 (greater than 5), so you round up to 5000. Your estimated number, 5000, is greater than the actual product.

The purpose of rounding and estimation is to simplify calculations and analyze systems or data without being bogged down by specificities.

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Answer:

4.9

Step-by-step explanation:

165.1-160.2

Answer:

I think the simplified answer is 7.69

value of x is: [tex]x=\frac{-31}{12}[/tex]

Step-by-step explanation:

We need to solve the equation f(x)=g(x)

where [tex]f(x)=(\frac{1}{2})^2-3[/tex]

and [tex]g(x) = 3x + 5[/tex]

Solving to find f(x)=g(x)

Putting values of f(x) and g(x)

[tex]f(x)=g(x)\\(\frac{1}{2})^2-3=3x + 5\\\frac{1}{4}-3=3x + 5\\Subtarct\,\,5\,\,on\,\,both\,\,sides:\\\frac{1}{4}-3-5=3x + 5-5\\\frac{1}{4}-8=3x\\Taking\,\,LCm\,\,on\,\,left\,\,side\\\frac{1-8*4}{4}=3x\\\frac{-31}{4}=3x\\Divide\,\,both\,\,sides\,\,by\,\,3\\x=\frac{-31}{4*3}\\x=\frac{-31}{12}[/tex]

So, value of x is: [tex]x=\frac{-31}{12}[/tex]

The graph will be a straight line x= -2.58 or x = -31/12

Keywords: Composition of Functions

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Answer:

120

Step-by-step explanation:

87.5% of what number is 105?

87.5%=0.875

105/0.875=120

Final answer:

The sum of the two weights, 13 lb 7 oz and 10 lb 2 oz, is 23 lb 9 oz. You add the ounces first, which don't need conversion, and then add the pounds.

Explanation:

Adding Pounds and Ounces

The question involves adding two weights together that are given in pounds and ounces. To do this, we need to add the ounces together first and then the pounds. The sum of 7 ounces and 2 ounces is 9 ounces. Since there are 16 ounces in one pound, we have no need to convert these ounces to pounds. The sum of 13 pounds and 10 pounds is 23 pounds. Therefore, when we combine these two sums, we arrive at the total weight of 23 pounds and 9 ounces.

Answer: No

Step-by-step explanation: because

1/2 +1/4 +1/3 is larger than one bowl.

6+3+4/12 = 13/12

;. 1 ¹/12.

Therefore, 1 bowl can not carry it

No, One bowl can not carry all of the ingredients at one time.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Chad made a snack by combining 1/3 of a bowl of granola with ¼ of a bowl of chopped banana and ½ of a bowl of yogurt.

The total amount 1/2 +1/4 +1/3 is larger than one bowl.

6 + 3 + 4/12 = 13/12

also 1 ¹/12.

Therefore, No 1 bowl can not carry it.

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Answer:

Standard Form : 3x+1y=35

Step-by-step explanation:

The equation of the line will be 3x+y-35=0

The equation of the line in standard form will be expressed by using the coefficient of x and coeficient of y which is given

ax+by+c=0

The equation of line which passes through two points will be

(y-y₁)/(x-x₁)=(y₂-y₁)/(x₂-x₁)

So according to asked question,

x₁=10,y₁=5

x₂=13,y₂=-4

the equation of line will be

(y-5)/(x-10)=(-4-5)/(13-10)

⇒(y-5)/(x-10)=-9/3

⇒(y-5)/(x-10)=-3

⇒y-5=-3(x-10)

⇒y-5=-3x+30

⇒y+3x-5-30=0

⇒3x+y-35=0

Therefore the equation of the line will be 3x+y-35=0

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Answer: 240 km

Step-by-step explanation:

From the graph :

50 miles = 80km

1 miles = 80/50 km

Therefore :

150 miles = 80/50 x 150

150 miles = 240 km

Answer:

1. k = 3

2. k = 5

Step-by-step explanation:

1. The graph shows two parallel lines intersecting y-axis:

The graph of the function g(x) is translated 5 - 2 = 3 units up graph of the function f(x). Thus, k = 3.

2.  The graph shows two parallel lines intersecting y-axis:

The graph of the function g(x) is translated 3 - (-2) = 5 units up graph of the function f(x). Thus, k = 5.

Answer:

$73

Step-by-step explanation:

Multiply 7 and 7 to get 49. Next, multiply 6 and 4 to get 24. The museum is free for the 3 children so you do not have to do anything. Add 49 and 24 to get 73, which is the price for the Baker Family.

Answer:

16 is x<3

Step-by-step explanation:

4x-10<2

Add 10 to both sides

4x<12

Divide 4 from both sides and you get x<3

Answer:

100 seconds

Erica and Amy are at distance of 1 km in 100 seconds

Step-by-step explanation:

They both are travelling in opposite directions so the sum of the distances they travel is the distance between them.

Let's take t as the total time taken to achieve a seperation of 1km

Distance traveled by Erica , (Speed of Erica - v1)

x1 = v1 * t

Distance travelled by Amy , (Speed of Amy - v2)

x2 = v2*t

Therefore sum of the distances they traveled is x1+x2 = x

x = v1*t + v2*t

x = t*(v1 + v2)

Here it is given that final seperation between Amy and Erica is 1km or 1000 m

Therefore x = 1000 m

Thus t = [tex]\frac{x}{v1+v2}[/tex]

Substituting given values v1 = 6 m/s v2 = 4 m/s

Therefore,

They are apart by exactly 1km in a time of 100 sec

Answer:

$4.25

Step-by-step explanation:

Ratio:

2.79:16.4 = x:25

16.4 × x

2.79 × 25

Cross multiply: 16.4x = 69.75

Then divide: 69.75 ÷ 16.4 = $4.25

Answer:

Step-by-step explanation:

[tex]x\div9=157\\\\\dfrac{x}{9}=157\qquad\text{multiply both sides by 9}\\\\9\!\!\!\!\diagup^1\cdot\dfrac{x}{9\!\!\!\!\diagup_1}=(9)(157)\\\\x=1413[/tex]

Answer:

No Solution.

Step-by-step explanation:

2(x-1)-y=-8

y=2x+8

----------------

2x-2-(2x+8)=-8

2x-2-2x-8=-8

2x-2x-2-8=-8

0-2-8=-8

-2-8=-8

-10=-8

no solution