If the measure of arc CB is 8/3 units, what is the measure of CAB?

Answer  1 2/7  divided by - 2 1/4 = -4/7

Result in decimals: -0.57142857142857

Step-by-step explanation:

\(\left| \log_7(x^8)\cfrac{}{} \right|~~ - ~~\left( ~~ \log_{49}(x^2) ~~ \right)^2 = 7 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \left| \log_7(x^8)\cfrac{}{} \right|\implies \pm\log_7(x^8)\implies \pm 8\log_7(x) \\\\[-0.35em] ~\dotfill\\\\ \left( ~~ \log_{49}(x^2) ~~ \right)^2\implies \left( ~~ \cfrac{\log_7(x^2)}{\log_7(49)} ~~ \right)^2\implies \left( ~~ \cfrac{\log_7(x^2)}{\log_7(7^2)} ~~ \right)^2\)

\(\left( ~~ \cfrac{\log_7(x^2)}{2} ~~ \right)^2\implies \left( ~~ \frac{1}{2}\log_7(x^2) ~~ \right)^2\\\\\\ \left( ~~ \log_7(x^{2\cdot \frac{1}{2}}) ~~ \right)^2 \implies \left( ~~ \log_7(x) ~~ \right)^2 \\\\[-0.35em] ~\dotfill\\\\ \left| \log_7(x^8)\cfrac{}{} \right|~~ - ~~\left( ~~ \log_{49}(x^2) ~~ \right)^2=7 \implies \pm 8\log_7(x)~~ - ~~\left( ~~ \log_7(x) ~~ \right)^2=7 \\\\[-0.35em] ~\dotfill\\\\ \textit{now let's make }\hspace{5em}\log_7(x)=Z \\\\[-0.35em] ~\dotfill\)

\(\mp 8Z-Z^2=7\implies 0=Z^2\pm 8Z+7\implies 0= \begin{cases} Z^2+ 8Z+7\\ Z^2 - 8Z+7 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 0=Z^2+8Z+7\implies 0=(Z+7)(Z+1)\implies 0=[\log_7(x)+7][\log_7(x)+1] \\\\\\ 0=Z^2-8Z+7\implies 0=(Z-7)(Z-1)\implies 0=[\log_7(x)-7][\log_7(x)-1]\)

now, let's process for each case to get its roots

\(0=\log_7(x)+7\implies -7=\log_7(x)\implies 7^{-7}=7^{\log_7(x)}\implies \boxed{7^{-7}=x} \\\\\\ 0=\log_7(x)+1\implies -1=\log_7(x)\implies 7^{-1}=7^{\log_7(x)}\implies \boxed{7^{-1}=x} \\\\\\ 0=\log_7(x)-7\implies 7=\log_7(x)\implies 7^{7}=7^{\log_7(x)}\implies \boxed{7^{7}=x} \\\\\\ 0=\log_7(x)+1\implies 1=\log_7(x)\implies 7^{1}=7^{\log_7(x)}\implies \boxed{7=x}\)

Answer:

3

Step-by-step explanation:

Who cares? just copy down the answer.

Answer:

we can describe this by using the formulas of Trigonometric functions..........Thank u.....

The sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

To translate the inequality expression "2/3y - 9 < y + 1" into a sentence, we can break it down into smaller parts:

"2/3y" represents two-thirds of a number.

"9" represents the number nine.

"y + 1" represents the number increased by one.

Now let's construct the sentence:

"Nine less than two-thirds of a number" - This refers to the expression "2/3y - 9," indicating that we have subtracted nine from two-thirds of a number.

"is less than" - This is the comparison symbol in the inequality.

"the number" - This refers to the expression "y + 1," representing the number increased by one.

Combining these parts, we form the sentence: "Nine less than two-thirds of a number is less than the number."

Hence, the correct sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

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Answer:

We are given that 50% of the ELTs are made by Company A, 45% are made by Company B, and 5% are made by Company C. We also know the rate of defects for each company's ELTs: 4% for Company A, 6% for Company B, and 9% for Company C.

Let D be the event that an ELT is defective, and let Bi be the event that an ELT was made by Company i, where i = A, B, or C. We want to find the probability that an ELT is made by Company B given that it is defective, i.e., we want to find P(B|D).

Using Bayes' theorem, we can write:

P(B|D) = P(D|B) * P(B) / P(D)

where P(D|B) is the probability that an ELT made by Company B is defective, P(B) is the prior probability that an ELT is made by Company B, and P(D) is the overall probability of an ELT being defective.

We can calculate each of these probabilities as follows:

P(D|B) = 0.06 (given)

P(B) = 0.45 (given)

P(D) = P(D|A) * P(A) + P(D|B) * P(B) + P(D|C) * P(C)

= 0.04 * 0.5 + 0.06 * 0.45 + 0.09 * 0.05

= 0.0355

Substituting these values into Bayes' theorem, we get:

P(B|D) = P(D|B) * P(B) / P(D)

= 0.06 * 0.45 / 0.0355

≈ 0.762

Therefore, the probability that an ELT made by Company B is defective given that it is found to be defective is approximately 0.762, or 76.2%.

Answer:

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

There are various combinations of coins.

In total there are:

The solution to the equation is given as option C

The equation says \(\frac{6}{5}+\frac{3}{5}x\)

we have to add the fractions

\(\frac{1 *6 +1*3x}{5}\)

= 6 + 3x / 5

Hence the correct solution to the question here is option C because\(\frac{6+3x}{5} = \frac{3}{5}(2+x)\)

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Answer:

a = 180° - 77° = 103°

hence , a = 103°

Answer: It would be the first one (20 pens for 8$)

Step-by-step explanation: If you divide 20 by 8 then each pencil will be 2.50$. However if you divide 30 by 10 it will be 3 dollars for each pencil so the first deal will be better since you spend less money.

The answer for lateral surface area of the Triangular prism is 180 cm²

Any solid object's lateral area can be calculated using the lateral area formula. Any figure's lateral area only includes the non-base faces. Calculating the lateral surface area of various forms, such as the cuboid, cube, cylinder, cone, and sphere, is made easier using lateral area formulas.

The lateral area for a triangular prism

A triangular prism's lateral area is equal to the sum of its side faces' areas (which are 3 rectangles). Specifically, it is the total surface area less the surface areas of the two bases. Additionally called the lateral surface area (LSA). Due to the two dimensions involved in its calculation, we measure it in square units.

The total of the three regions is the triangular prism's lateral area. Consequently, the triangular prism's lateral area formula is

Triangular prism lateral surface area (LSA) = ah + bh + ch (or) (a + b + c) h.

We are aware that the perimeter of the base is (a + b + c) (triangle). Hence,

Triangular prism's lateral surface area (LSA) is equal to the product of the base's perimeter and the prism's height.

base perimeter × height

Explanation

The Given Image of the solid is Matching to a prism.so we are calculating the lateral surface area of the prism

The dimensions of each base are:

a = 5cm

b = 4 cm

c = 3 cm

The height of the triangular prism = 15cm.

Thus, the lateral area of triangular prism = (a + b + c ) h

= (5 + 4 + 3) 15

= (12) 15

= 180 cm²

Answer: The lateral area of the given triangular prism = 180 cm²

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Answer:

8.60cm

Step-by-step explanation:

a/sinA=b/sinB

15/sin90⁰=x/sin35⁰

cross multiply

15sin35⁰=xsin90⁰

8.6036=x

x=8.60cm

Answer:

Step-by-step explanation:

Given triangle is isosceles:

It makes opposite angles equal too:

One angle measure is given:

Find the other interior angles:

Since all interior angles are equal, all sides are equal too:

It's a equilateral triangle as 1 side is 60°.Other two angles are equal and will be 60°.

\(\\ \tt\longmapsto 2x-1=3x-7\)

\(\\ \tt\longmapsto -1+7=3x-2x\)

\(\\ \tt\longmapsto 6=x\)

The difference in overall gain between selling stock A at the current day's high price or low price and selling stock B at the current day's high price or low price is $239.50.

To determine the difference in overall gain or loss between selling stock A at the current day's high price or low price and selling stock B at the current day's high price or low price, we need to calculate the selling prices of the stocks.

Stock A:

High price = $105.19

Low price = $103.25

Close price = $103.38

Stock B:

High price = $145.18

Low price = $143.28

Close price = $144.05

The investor purchased 50 shares of stock A at $90 per share and 75 shares of stock B at $145 per share.

To calculate the selling prices, we need to multiply the number of shares by the respective selling price.

Selling price of stock A at the high price: 50 shares \(\times\) $105.19 = $5,259.50

Selling price of stock A at the low price: 50 shares \(\times\) $103.25 = $5,162.50

Selling price of stock B at the high price: 75 shares \(\times\) $145.18 = $10,888.50

Selling price of stock B at the low price: 75 shares \(\times\) $143.28 = $10,746.00

Now, let's calculate the difference in overall gain or loss:

Difference in overall gain = Selling price at the high price - Selling price at the low price

= ($5,259.50 + $10,888.50) - ($5,162.50 + $10,746.00)

= $16,148.00 - $15,908.50

= $239.50

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Answer:

The probability is 0.58992 or simply 0.59

Step-by-step explanation:

We start by getting the z-scores of the diameter

we have this as follows;

Mathematically;

z-score = (x-mean)/SD

mean = 9.0 mm

SD = 1.5 mm

For 8.00 mm, we have

z = (8-9)/1.5 = -0.67

For 10.5 mm, we have

z = (10.5-9)/1.5 = 1

So the probability we want to calculate is;

P( 1 < x < -0.67)

we can calculate this using the standard normal distribution table

We have this as ;

P( x < -0.67) - P( x > 1) = 0.58992

Answer:

-11

Step-by-step explanation:

Notice how

\(f(x)=x^{2} +8x+1\)

So when we have

\(f(-6)=(-6)^{2} +8(-6)+1= 36-48+1=-11\)

The answer is:

f(-6) = -11

Step-by-step explanation:

Plug in -6 for x:

\(\sf{f(x)=x^2+8x+1}\)

\(\sf{f(-6)=(-6)^2+8(-6)+1}\)

Simplify this:

\(\sf{f(-6)=36-48+1}\)

\(\sf{f(-6)=-12+1}\)

\(\sf{f(-6)=-11}\)

If a linear function is increasing, the reciprocal function must be decreasing, mathematically because the reciprocal function is the inverse of the linear function

The reciprocal function of a linear function is given by the formula:

f(x) = 1/x

If a linear function is increasing, then its slope (m) is positive. This means that the slope of the reciprocal function must be negative. The slope of the inverse of a linear function is the negative reciprocal of the slope of the linear function, meaning that the slope of the reciprocal function must be negative for the linear function to be increasing.

To illustrate this, we can consider a simple example of a linear function, f(x) = 2x. This linear function has a positive slope (2), so its reciprocal function, f(x) = 1/x, must have a negative slope (-1). This means that the reciprocal function is decreasing.

In general, if a linear function is increasing, then its reciprocal function must be decreasing, as the slope of the reciprocal function must be the negative reciprocal of the slope of the linear function.

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The answer of the given question based on the Velocity is,  times are t = 1.00 seconds and t = 0.12 seconds, respectively.

Velocity is a vector quantity that describes the rate of change of an object's position with respect to time. In other words, it tells us how fast and in what direction an object is moving. Velocity is typically measured in units of distance per time, such as meters per second (m/s) or feet per second (ft/s).

To find the time(s) when the ball's height is 7 feet, we can substitute h = 7 into the equation for the ball's height and solve for t:

7 = 3 + 17t - 16t²

Rearranging and setting the equation equal to zero, we get:

16t^2 - 17t + 4 = 0

We can solve for t by using the quadratic formula:

t = (-b ± √(b² - 4ac)) / 2a

where a = 16, b = -17, and c = 4. Plugging in these values, we get:

t = (-(-17) ± √((-17)² - 4(16)(4))) / 2(16)

t = (17 ± √(225)) / 32

t = (17 + 15) / 32 or t = (17 - 15) / 32

t = 1 or t = 1/8

Therefore, the ball's height is 7 feet at times t = 1 second and t = 1/8 seconds. Rounded to the nearest hundredth, these times are t = 1.00 seconds and t = 0.12 seconds, respectively.

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Answer:we cant really answer this without the image

Step-by-step explanation:

Answer: 3, -4

Step-by-step explanation: gust look harder

Answer:

-19\(x^{2}\) + 8x + 6

Step-by-step explanation:

−12\(x^{2}\)−5x−7\(x^{2}\)+6+13x

= −12\(x^{2}\)−7\(x^{2}\)+13x-5x+6

= -19\(x^{2}\) + 8x + 6

Answer:

x is first angle

y is second angle

and z is third angle

Step-by-step explanation:

This question is solved by a system of equations. We have that:x is the first angle.y is the second angle.z is the third angle.Doing this, we get that:The first angle measures 30º.The second angle measures 67º.The third angle measures 83º.The sum of the measures of the angles of a triangle is 180. This means that The sum of the measures of the second and third angles is five times the measure of the first angle.This means that:From this, the first angle can be found:The measure of the first angle is of 30º.The third angle is 16 more than the second.This means that:Since We get that the second angle is:The second angle measures 67º.For the third angle:The third angle measures 83º.

Radius=1/2 of Diameter

radius=1/2×50

radius=25

Volume of Sphere= 4/3 pie r^3

=4/3×22/7×25×25×25

=4/3×3.14×625×25

=4/3×3.14×16625

=4/3×52202.5

=4×17400.83

=69603.32

Volume of Sphere is 69603.32 sq.cm^3

The answer will be 13 km that is displacement of the car.

What is displacement?

When a body shifts from one position to another, displacement is the smallest (straight line) distance between the starting position and the ending position of the body, which is symbolized by an arrow pointing from the starting position to the ending position. Displacement is a vector quantity that describes "how far out of place an object is"; it represents the overall change in the position of the object.

A car travels 12 km north and turns left to travel 5km.

So the final position of car from the initial position is :

So the placement of the car is √(12²+5²) = √169 =13km

Hence the Displacement of the car is 13 km

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The sample consists of 949 elderly people and the population is all elderly people both options are correct and the numbers 22% and 17% represent the sample statistics.

a.

The set that includes the list of all possible individuals in the interesting area of study is termed a population while the portion or a part of the population is termed a sample. The given scenario indicates that the population is all elderly people from which 949 elderly people are selected for the study and so, 949 elderly people are included in the sample. So, option 1 and option 2 are correct for the indicated scenario.

b.

The percentages 22% and 17% are calculated from 949 elderly people that are indicated as samples. Hence, the percentages 22% and 17% are the measure of the sample and so, they represent sample statistics.

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If the quotient of c and −19 is 38 then the value of c is -722.

A division is a process of splitting a specific amount into equal parts. 

We have,

The quotient of c and −19 is 38.

This means that if we divide c by -19 the quotient is 38.

Quotient = 38

Divisor = -19

Dividend = c

The remainder is not given so we assume it to be zero.

Remainder = 0

We have a formula for the division of two numbers.

Dividend ÷ Divisor = Quotient + Remainder

c ÷ -19 = 38 + 0

c/-19 = 38

c = 38 x -19

c = -722

Thus,

If the quotient of c and −19 is 38 then the value of c is -722.

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