2c +3= -11
Remember:

On solving this trigonometry, we find that (a) sec(sin⁻¹ \(\frac{12}{13}\)) = \(\frac{13}{5}\) and (b) tan(sin⁻¹ \(\frac{12}{13}\)) = \(\frac{12}{5}\)

(a) To find the exact value of sec(sin⁻¹ \(\frac{12}{13}\)), we can use the fact that sec(x) = \(\frac{1}{cos}\)(x). Let's draw a right triangle with opposite side 12 and hypotenuse 13. Using the Pythagorean theorem, we can find the adjacent side:

a² + b² = c²

a² + 12² = 13²

a² = 169 - 144

a = √25

a = 5

So our triangle has sides of length 5, 12, and 13. Now we can find cos(sin⁻¹  \(\frac{12}{13}\)) by looking at the adjacent/hypotenuse ratio in this triangle:

cos(sin⁻¹ \(\frac{12}{13}\)) =  \(\frac{5}{13}\)

Therefore, sec(sin⁻¹(12/13)) = 1/cos(sin⁻¹ \(\frac{12}{13}\))

                                            = 1/\(\frac{5}{13}\)

                                            = \(\frac{13}{5}\).

So the exact value of sec(sin⁻¹ \(\frac{12}{13}\)) is \(\frac{13}{5}\).

(b) To find the exact value of tan(sin⁻¹ \(\frac{12}{13}\)), we can use the fact that tan(x) = sin(x)/cos(x). Let's use the same right triangle as before.

Then sin(sin⁻¹ \(\frac{12}{13}\))=  \(\frac{12}{13}\) and cos  \(\frac{12}{13}\)) = \(\frac{5}{13}\)  , so

tan(sin⁻¹ \(\frac{12}{13}\)) = sin(sin⁻¹ \(\frac{12}{13}\))/cos(sin⁻¹\(\frac{12}{13}\))

                        = \(\frac{12}{13}\) / \(\frac{5}{3}\)

                        = \(\frac{12}{5}\)

So the exact value of tan(sin⁻¹ \(\frac{12}{13}\)) is \(\frac{12}{5}\).

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Answer:

awnser one is 7 and question 2 is -10

Step-by-step explanation:

−12−2−−55=?  question one

In the first fraction, the negative numerator and negative denominator cancel each other.

Since the the second fraction is negative and you are subtracting, remove the negative sign and switch the operation to addition.

The equivalent equation is

122+55=?

The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

LCD(12/2, 5/5) = 10

Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.

(122×55)+(55×22)=?

Complete the multiplication and the equation becomes

6010+1010=?

The two fractions now have like denominators so you can subtract the numerators.

Then:

60+1010=7010

Since 70 divided by 10 equals 7 then,

7010=7

Therefore:

−12−2−−55=7    

Question 2

−81+6−3=?

In the second fraction, move the negative sign from the denominator to the numerator and the value remains the same.

The equivalent equation is

−81+−63=?

The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

LCD(-8/1, -6/3) = 3

Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.

(−81×33)+(−63×11)=?

Complete the multiplication and the equation becomes

−243+−63=?

The two fractions now have like denominators so you can add the numerators.

Then:

−24+−63=−303

Since -30 divided by 3 equals -10 then,

−303=−10

Therefore:

−81+6−3=−10

Solution by Formulas

Apply the fractions formula for addition, to

−81+6−3

and solve

(−8×−3)+(6×1)1×−3

=24+6−3

=30−3

=−10

The ratio strength of the final product is 1:0.4.

One technique to indicate concentration is through ratio strength, which uses a ratio to characterize drug concentration. In this context, concentration is defined as the quantity of a solute that makes up one unit in the whole volume of a solution or combination. You should be an expert in ratio strength calculations as a pharmacy student. Ratio strength uses a ratio to describe the medication concentration. So, what it implies is, you have one unit of solute contained in the complete amount of preparation and so generally your ratio strength is expressed as one is to something. In the case of a weight-in-weight, volume-in-volume, or weight-in-volume situation, you would interpret a ratio of 1:2,000 differently.

Drug strength = 800mg

whole volume =2ltrs

The ratio of the solution in 1 ltr is = 400 mg

The ratio strength of the solutions is = 1:0.4

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Answer:

Yes, there's a solution. x=1, y=0

Step-by-step explanation:

-2x+2=2x-2

4x=4

x=1

y=2×1-2=0

So, the basketball player needs to shoot the ball with a velocity of u so that the maximum height attained by the ball is 10.0625 feet.

Given, A basketball player shoots a foul shot, releasing the ball at a 45-degree angle from a position 6 feet above the floor, then the path of the ball can be modeled by the quadratic function,

h(x) = -0.005x² + 0.45x + 6

Here, the ball has released at an angle of 45 degrees, then the vertical velocity (v) and horizontal velocity (u) can be given as:

v = usinθ = ucosθ = gt...

As the projectile motion is a 2-D motion]where t is the time, g is the acceleration due to gravity.

As the maximum height is attained at the mid of the total time taken, thus the time taken to attain the maximum height (H) can be given as:

H = u sin(θ)/g

So, H = u/g [Here, sin(θ) = 1/root2]

Also, The total time (T) of flight can be given as:

T = 2u sinθ/g

We can calculate the value of T using the formula above.

T = 2u sinθ/g

= 2u(1/root2)/g

= u/g√2

Now, Let's put the value of T in the quadratic equation of the path of the ball,h(x)

= -0.005x² + 0.45x + 6h(x)

= -0.005(x² - 90x) + 6h(x)

= -0.005(x²- 90x + 2025 - 2025) + 6h(x)

= -0.005((x - 45)²- 1012.5) + 6h(x)

= -0.005(x - 45)² + 10.0625

As the vertex of the parabola represents the maximum height, thus the maximum height (H) can be given as, H

= 10.0625 feet

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Answer:

There are 0.454 kg in one pound.

So, in 120 pounds there are 0.454 x 120 kgs.

This is equal to 54.48, and the answer is 54.48 kg.

Let me know if this helps!

Answer:

20 cents per unit

Step-by-step explanation:

Since it is 1$ 5 pencils and 100/5=20, the unit cost is 20 cents

Answer:

the unit price is $0.20 for 1 pencil

Step-by-step explanation:

if u see 5 pencils cost 1 dollars and unit price means the value of one item, so like the cost of 1 pencil

write it as a ration of cost to pencil

the ratio is 1/5

now divided 5 on the top and the bottom to get the unit price

1 divided by 5= 0.2

so now the ratio is 0.2/1

The value of the test​ statistic is - 0.462.

A standard deviation (or) would be a way of measuring of how widely distributed the data has been in relation towards the mean. A low standard deviation indicates that data is grouped around the mean, whereas a high standard deviation indicates that data is more spread out.

The null hypothesis is:

H0 = 0.25

The alternate hypothesis is:

H1 does not equal to 0.25,

the general formula for standard deviation is :-

σ=√1N∑Ni=1(Xi−μ)2 σ = 1 N ∑ i = 1 N ( X i − μ ) 2.

Our test statistic is:

t = (x- u) /s

In which X is the sample mean,  u is the population mean(the null hypothesis),   s is the standard deviation of the sample.

According to question,

x = 23/100

x = 0.23

u = 25/100

u= 0.25

s= √(0.25 * 0.75)/100

s = 0.0433

so for the value of t,

standard deviation = (x - u)/t

so , t=  (x- u) /s

t = (0.23 - 0.25)/0.0433

t = - 0.462

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Answer:

adult-135

kid-27

Step-by-step explanation:

13.50*10=135

4.50*6=27

Answer:  

\(log_b(w^3y^4)\)

Step-by-step explanation:

To write the expression as a single logarithm, or condense it, use the properties of logarithms.  

1) The power property of logarithms states that \(log_ax^r = rlog_ax\). In other words, the exponent within a logarithm can be brought out in front so it's multiplied by the logarithm. This means that the number in front of the logarithm can also be brought inside the logarithm as an exponent.  

So, in this case, we can move the 3 and the 4 inside the logarithms as exponents. Apply this property as seen below:

\(3log_bw+4log_by\\=log_bw^3+log_by^4\)

2) The product property of logarithms states that \(log_axy = log_ax+log_ay\). In other words, the logarithm of a product is equal to the sum of the logarithms of its factors. So, in this case, write the expression as a single logarithm by taking the log (keep the same base) of the product of \(w^3\) and \(y^4\). Apply the property as seen below and find the final answer.  

\(log_bw^3+log_by^4\\=log_b(w^3y^4)\)

So, the answer is \(log_b(w^3y^4)\).

Answer:

-1 is 1 to the left of zero. Positive one is 1 to the right of zero

Step-by-step explanation:

Answer:

\(r =\bf 8 \space\ cm\)

Step-by-step explanation:

The formula for volume of a cylinder is as follows:

\(\boxed{Volume = \pi r^2 h}\)

where:

• r = radius (? cm)

• h = height (7 cm).

Substituting the values into the formula:
\(448 \pi = \pi \times r^2 \times 7\)

Now solve for \(r\):

⇒ \(r^2 = \frac{448 \pi }{\pi \times 7}\)

⇒ \(r = \sqrt{64}\)

⇒ \(r =\bf 8 \space\ cm\)

\( \huge\mathbb{ \underline{SOLUTION :}}\)

Given:

\(\longrightarrow\sf{V= \pi r^2 h}\)

\(\longrightarrow\sf{448 \pi= \pi r^2 \cdot 7}\)

\(\longrightarrow\sf{448=

7r^2}\)

\(\longrightarrow\sf{r^2= \dfrac{448}{7} }\)

\(\longrightarrow\sf{r^2=64}\)

\(\huge \mathbb{ \underline{ANSWER:}}\)

\(\longrightarrow\sf{r= 8cm}\)

Answer:

The only point that satisfies both equations simultaneously is (3, 0).

Step-by-step explanation:

To determine which point is a solution to the given system of linear equations, we need to substitute the coordinates of each point into the equations and see which point(s) satisfy both equations simultaneously.

Given system of linear equations:

y = −x + 3

x − 3y = 3

Substituting the coordinates of each point, we get:

(0, 3):

y = −x + 3 => 3 = -0 + 3 => 3 = 3 (satisfied)

x − 3y = 3 => 0 - 9 = 3 => -9 ≠ 3 (not satisfied)

(1, 2):

y = −x + 3 => 2 = -1 + 3 => 2 = 2 (satisfied)

x − 3y = 3 => 1 - 6 = 3 => -5 ≠ 3 (not satisfied)

(3, 0):

y = −x + 3 => 0 = -3 + 3 => 0 = 0 (satisfied)

x − 3y = 3 => 3 - 0 = 3 => 3 = 3 (satisfied)

(4, −1):

y = −x + 3 => -1 = -4 + 3 => -1 = -1 (satisfied)

x − 3y = 3 => 4 - (-3) = 3 => 7 ≠ 3 (not satisfied)

Therefore, the only point that satisfies both equations simultaneously is (3, 0).

Answer:

1/8

Step-by-step explanation:

50% of 1/4 = 1/8

hope this helps!

Answer:

1/8

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

You go to the point a1,2 ant take out the cross that intersects there. you then find the determinant

[12 24 ]

[-4 -7 ]

12(-7) - (-4)(24)

-84-(-96)

-84+96=12

I hope this helps, not sure what the whole question or the directions where but this is what i got from what you gave me. good luck!

Answer:

5

Step-by-step explanation:

f(1)=8

f(2)=1/2(8)+2=6

f(3)=1/2(6)+2=5

Answer:

look at the picture .................

9514 1404 393

Answer:

  7.56 cm

Step-by-step explanation:

The volume is given by the formula ...

  V = 1/3b²h . . . . where b is the base edge length, and h is the height.

Here we have V = 144 cm³, and b = h. Filling in these values and solving for h, we get ...

  144 cm³ = 1/3h³

  432 cm³ = h³

  h = ∛432 cm ≈ 7.55953 cm

The height of the pyramid is about 7.56 cm.

Answer:

\(7.56cm\)

Step-by-step explanation:

Given that,

base length = Height

so,

\(volume = \frac{1}{3} {b}^{2} h \\ \)

We can also write this as( according to this question)

\(v = \frac{1}{3} \times {b}^{2} \times b \\ v = \frac{ {b}^{3} }{3} \)

let's solve

\(v = \frac{ {b}^{3} }{3} \\ 144 = \frac{ {b}^{3} }{3} \\ 144 \times 3 = {b}^{3} \\43 2 = {b}^{3} \\ \sqrt[3]{432} = b \\ b = 7.55\)

\(base = height = 7.55cm \\ \)

= 7.56cm

To find the constant of proportionality:

We can see that for every 1 unit we move to the right on the x- axis (positive), the line moves up 2 units.

Divide the change on y by that change on x:

2/1=2

The constant of proportionality is 2. (option a)

Answer:

1,056

Step-by-step explanation:

16 x 6 = 96

96 x 11 = 1,056

Hey there!

16 * 6 * 11

16 * 6

= 16 + 16 + 16 + 16 + 16 + 16

= 32 + 32 + 32

= 64 + 32

= 96

= 96 * 11

= 96 * 11

= 96 + 96 + 96 + 96 + 96 + 96 + 96 + 96 + 96 + 96 + 96

= 192 + 192 + 192 + 192 + 192 + 96

= 384 + 384 + 288

= 768 + 288

= 1,056

Therefore, your answer is: 1,056

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

4

Step-by-step explanation:

In functions, value of x = 45 and y = 45

What is function in math?

6)  x = 15

 y = 49

3x = 3 * 15 = 45

y - 4 = 49 - 4 = 45

7)  3x + 23 = 4x

    4x - 3x = 23

     x = 23

    y =  4 * 23 =   92°

8) y + 12 = 5x °

  3x + 50  =

According to the question

     y + 12 = 3x  + 50

      5x   = 3x + 50

      2x = 50

        x = 25

y + 12 = 5x °

y = 5 * 25 - 12

y = 125 - 12 =   113

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The 45th term of the sequence is 267.

The 45th term of a sequence can be calculated using the formula:

Tn = a + (n – 1)d

Where,

Tn = the nth term

a = the first term

n = the term position

d = the common difference

In this sequence, the first term is 3, the common difference is 6, and the term position is 45.

Therefore, the 45th term of the sequence is:

T45 = 3 + (45 – 1)6

T45 = 3 + (44)6

T45 = 3 + 264

T45 = 267

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Answer:

4656.46km

Step-by-step explanation:

Given that:

Abuja (Nigeria) = (9°N,7°E)

Bonn (Germany) = (51°N,7°E)

Longitudinal difference = 51 - 9 = 42°

Radius of the earth (R) = 6400

Distance = θ/360 * 2πr

r = Rcos7° = 6400 * cos7 = 6352.2953

Hence,

Distance = (42/360) * 2 * 3.142 * 6352.2953

Distance = 0.1166666 * 2 * 3.142 * 6352.2953

Distance = 4656.4757 km

Answer:

7.2 miles

Step-by-step explanation:

52-16= 36

36/5= 7.2

Answer:

97 meters

Step-by-step explanation:

The area of a rectangle is its length multiplied by its width. Substitute the known values into this equation and solve for the length, l:

a = lw

8342 = 86l

l = 97

We can calculate the values and find the number of payments (N). Then, we divide N by 26 to get the number of years it will take George to pay off the mortgage. 2.4988 / log(1 + r') is the final solution.

To determine the number of years it will take George to pay off the mortgage, we can use the formula for the number of payments required to pay off a loan. The formula is given by:

N = (log(PV/A)) / (log(1 + r)),

where:

N is the number of payments,

PV is the present value of the loan (mortgage amount),

A is the payment amount,

r is the interest rate per payment period.

In this case, the mortgage amount (PV) is $130,000, the payment amount (A) is $413 every two weeks, and the interest rate (r) is 3.35% per year.

First, we need to convert the interest rate to the rate per payment period. Since the payment is made every two weeks, there are 26 payments in a year (52 weeks / 2 weeks).

The interest rate per payment period (r') can be calculated as follows:

r' = (1 + r)^(1/26) - 1,

where r is the annual interest rate.

Substituting the values, we have:

r' = (1 + 0.0335)^(1/26) - 1.

Next, we can plug the values into the formula to find the number of payments (N):

N = (log(130,000/413)) / (log(1 + r')).

Using a calculator, we can calculate the values and find the number of payments (N). Then, we divide N by 26 to get the number of years it will take George to pay off the mortgage.

2.4988 / log(1 + r') is the final solution.

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Answer without Explanation:

B

By visualizing the data on the scatter plot, you can determine if there is a relationship between the hours spent studying and the midterm grades.

Based on the given information, it appears that the hours spent studying and the corresponding midterm grades are being compared. To analyze the relationship between the two variables, you can create a scatter plot. Here are the steps to create the scatter plot:

Step 1: Arrange the data pairs in two columns, with hours spent studying in one column and midterm grades in the other column.

Step 2: Plot each data pair as a point on the graph. The hours spent studying will be represented on the x-axis, and the midterm grades will be represented on the y-axis.

Step 3: Connect the dots with a line or curve to see if there is any pattern or trend in the data.

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Answer:-

Angle N = 70, Angle M = 110

Step-by-step explanation:

This shape is a parallelogram.

Given, find the measure of Angle N and Angle M

We know that the adjacent angles of a parallelogram are supplementary (180°)

So the equation we form is:-

2x + 3x + 5 = 180

We can solve it like:-

2x + 3x + 5 = 180

5x + 5 = 180

5x = 180 - 5

5x = 175

x = 175 ÷ 5

x = 35

So, in the question, we have to find the measure of the angles.


Angle N = 2x = 2 x 35 = 70°

Angle M = 3x + 5 = 3 x 35 + 5 = 105 + 5 = 110°


We can also verify this by checking if the sum of these angles add up to 180°


110+70 = 180°


Hence, proved!

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