Which number is an integer?​

Answer:

The polynomial 90d^2 + 30d represents the total distance traveled in miles, not the speed. To find the average speed, we need to divide the distance traveled by the time taken.

If we have traveled for 15d hours, then the distance traveled is:

90d^2 + 30d miles

The average speed is:

(distance traveled) / (time taken) = (90d^2 + 30d) / (15d) = 6(15d^2 + 5d) / (15d) = 6(3d + 1) miles per hour

Therefore, the average speed is 6(3d + 1) miles per hour, or simply 18d + 6 miles per hour.

Answer:

B. RZ =R BZ

Step-by-step explanation:

Since point Z is equidistant from the sides of ARST, it lies on the perpendicular bisectors of both sides. Therefore, CZ and SZ are perpendicular bisectors of AB and ST, respectively.

Option B is true because point R lies on the perpendicular bisector of AB, and therefore RZ = RB.

Answer: vv

Step-by-step explanation:

Since point Z is equidistant from the sides of ARST, it lies on the perpendicular bisector of the sides ST and AR.

Therefore, we can draw perpendiculars from point Z to the sides ST and AR, which intersect them at points T' and R', respectively.

Now, let's examine the options:

A. SZ & TZ: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of ST, and the distance from Z to S and T could be different.

B. RZ = RB: This is true, as point Z lies on the perpendicular bisector of AR, and is therefore equidistant from R and B.

C. CTZ = ASZ: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of AR, and the distances from Z to C and A could be different.

D. ASZ = ZSB: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of ST, and the distances from Z to A and B could be different.

Therefore, the only statement that must be true is option B: RZ = RB.

AnswER:   MULTIPLYYY

Step-by-step explanation:

The total number of members of the club will be 128 members.

It should be noted that the total number of members of the club will be:

= 25 + 38 + 32 + 24 + 9

= 128

Also, the histogram has been completed and attached.

Learn more about histogram on:

brainly.com/question/2962546

#SPJ1

Answer:

0.6508

Step-by-step explanation:

The standard normal distribution has a mean μ= 1 and standard deviation σ = 0

The area under the normal curve for any z value say Z i.e. P(z ≤ Z) can be read off from the Standard Normal Tables or just use a statistical calculator

Using a calculator is best
I see the lower z score as - 2.61 and the upper z score as 0.4

P(-2.61 ≤ z ≤ 0.4) = P(0.4) - P(-2.61)

P(z ≤ 0.4) = 0.65542

P(z ≤ -2.6) = 0.0045271

P(z ≤ 0.4) - P(z ≤ -2.6)  = 0.65542 - 0.0045271  = 0.6507588 = 0.6508 rounded to 4 decimal places

(Note: some calculators are able to directly compute the area between two z values)

The A⁻¹ of the given matrix is \(\dfrac{1}{-12}\left[\begin{array}{cc}8&-4\\-2&-3\\\end{array}\right]\).

The inverse of the matrix is calculated by the ratio of the adjoint of the given matrix A to the determinant of the matrix A.

The inverse of a matrix is a matrix that, when multiplied by the original matrix, results in the identity matrix.

The formula to calculate the inverse of a matrix is,

\(A_{Adj}=\left[\begin{array}{cc}8&-4\\-2&-3\\\end{array}\right]\).

The determinant of the matrix is,

D = [ad - bc ]

D = [ (-3 x 8 ) - ( 4 x -2 ) ]

D = -12

The inverse of the matrix will be,

\(A^{-1}=\dfrac{1}{ab-bc}\left[\begin{array}{cc}d&-b\\-c&a\\\end{array}\right]\\A^{-1}=\dfrac{1}{(-3\times 8)-(4\times -2)}\left[\begin{array}{cc}8&-4\\2&-3\\\end{array}\right]\\\\A^{-1}=\dfrac{1}{-12}\left[\begin{array}{cc}8&-4\\2&-3\\\end{array}\right]\\\\\)

To know more about inverse matrix follow

https://brainly.com/question/12537023

#SPJ

Answer:

if boo ygdv

Step-by-step explanation:

f bi igfcnkyf f jurf

Answer:

7g + 3n - 2

Step-by-step explanation:

when you subtract you 'add the opposite'; subtracting a negative is the same as adding a positive

for example, using the above statement we can rewrite the problem as:

7g - 6 + 3n + 4

we can combine -6 and 4 to get -2

7g + 3n - 2 or 7g + 3n + (-2)

If a ≠ 0 and b = 0: The solution set is {0}. If a ≠ 0 and b ≠ 0: The solution set is {b/a}. If a = 0 and b ≠ 0: There are no solutions. If a = 0 and b = 0: The solution set is all real numbers.

The possible solution sets of the linear equation ax = b, where a and b are real numbers, depend on the values of a and b.

If a ≠ 0:

If b = 0, the solution is x = 0. This is a single solution.

If b ≠ 0, the solution is x = b/a. This is a unique solution.

If a = 0 and b ≠ 0:

In this case, the equation becomes 0x = b, which is not possible since any number multiplied by 0 is always 0. Therefore, there are no solutions.

If a = 0 and b = 0:

In this case, the equation becomes 0x = 0, which is true for all real numbers x. Therefore, the solution set is all real numbers.

In summary, the possible solution sets of the linear equation ax = b are as follows:

If a ≠ 0 and b = 0: The solution set is {0}.

If a ≠ 0 and b ≠ 0: The solution set is {b/a}.

If a = 0 and b ≠ 0: There are no solutions.

If a = 0 and b = 0: The solution set is all real numbers.

Learn more about real number :

https://brainly.com/question/10547079

#SPJ11

The matching numbers are:

1) 0.0000225 = 2 x 10⁻⁵

2) 219,000 = 2 x 10⁵

3) 3,40,000 = 3 x 10⁶

4) 297,000 = 3 x 10⁵

5) 0.0000034 = 3 x 10⁻⁶

What are Exponents?

The exponent of a number indicates how many times a number has been multiplied by itself. For instance, 34 indicates that we have multiplied 3 four times. Its full form is 3 3 3 3. Exponent is another name for a number's power. A whole number, fraction, negative number, or decimal are all acceptable.

We have to match the following terms :

1) 0.0000225 = 2 x 10⁻⁵
we can write 0.0000225 as
2.25 / 100000
or, 2.25 / 10⁵
then, 2.25 x 10⁻⁵

2) 219,000 =  2 x 10⁵
as the numbers after 2 are 5
therefore we write 10⁵

3) 3,40,000 = 3 x 10⁶
as the numbers after 3 are 6
therefore we write 10⁶

4) 297,000 = 3 x 10⁵
we round off 297 as 300
as the numbers after 3 are 5
therefore we write 10⁵

5) 0.0000034 = 3 x 10⁻⁶
we can write 0.0000034 as
3.4/ 1000000
or, 3.4 / 10⁶
then, 3.4x 10⁻⁶

Hence, the matching numbers are:
1) 0.0000225 = 2 x 10⁻⁵
2) 219,000 = 2 x 10⁵
3) 3,40,000 = 3 x 10⁶
4) 297,000 = 3 x 10⁵
5) 0.0000034 = 3 x 10⁻⁶

To learn more about Exponents click on the link
https://brainly.com/question/11975096
#SPJ1

To evaluate the given integral, the most helpful substitution is x = 15 sec θ. The rewritten integral will be dx = 15 sec θ tan θ dθ / (225 + 225 sec² θ)².

In trigonometric substitution, we choose a substitution that simplifies the integral by transforming it into a form that can be easily evaluated using trigonometric identities. In this case, the most helpful substitution is x = 15 sec θ.

To rewrite the integral, we need to express dx in terms of θ. Since x = 15 sec θ, we can differentiate both sides with respect to θ to find dx. The derivative of sec θ is sec θ tan θ, so we have dx = 15 sec θ tan θ dθ.

Substituting this expression for dx and rewriting (225 + x²)² in terms of θ, we obtain:

∫(x² dx) / (225 + x²)² = ∫[(15 sec θ)² (15 sec θ tan θ dθ)] / (225 + (15 sec θ)²)².

Simplifying further, we get:

∫(225 sec² θ tan θ dθ) / (225 + 225 sec² θ)².

This is the rewritten form of the integral using the substitution x = 15 sec θ.

Learn more about trigonometric substitution here:

https://brainly.com/question/32150762

#SPJ11

To find the possible values of k, we need to calculate the determinant of matrix D and set it equal to 1024.

Given matrix D:

D = | k 0 0 |

| 3 k² k³ |

| 0 kª k³ kº |

| k k k |

| 0 0 0 |

| k¹⁰ |

The determinant of D can be calculated by expanding along the first row or the first column. Let's expand along the first row:

det(D) = k(det | k³ k k |

| 0 k³ kº |

| 0 0 k¹⁰ |)

- 0(det | 3 k² k³ |

| 0 kª k³ |

| k k k |)

+ 0(det | 3 k² k³ |

| k k k |

| k k k |)

Simplifying further, we have:

det(D) = k(det | k³ k k |

| 0 k³ kº |

| 0 0 k¹⁰ |)

Now, we can calculate the determinant of the 3x3 submatrix:

det | k³ k k |

| 0 k³ kº |

| 0 0 k¹⁰ |

This determinant can be found by expanding along the first row or the first column. Expanding along the first row gives us:

det = k(k³(kº) - 0(k)) - 0(0(k¹⁰)) = k⁴kº = k⁴+kº

Now, we can set det(D) equal to 1024 and solve for k:

k⁴+kº = 1024

Since we are looking for all possible values of k, we need to solve this equation for k. However, solving this equation may require numerical methods or approximations, as it is a quartic equation.

Learn more about matrix here

https://brainly.com/question/2456804

#SPJ11

Answer:

i dont  know the answer but i think its 12

Step-by-step explanation:l

people are goof

The sum is 56

Here, we want to find the sum of the given expression

To do this, we need to evaluate what we have in each of the brackets and add up

Thus, we have that;

Answer:

y divided by k

Step-by-step explanation:

The linear trend equation to predict monthly receipts is given by: $$Y_{t}=3,700+300t$$ where Y is the predicted monthly receipt and t is the time period in months where t=0 is July this year.

To forecast the receipt for October, we need to find the value of Y when t=3 (since t=0 corresponds to July, August would be t=1, September would be t=2, and October would be t=3).Therefore, we can substitute t=3 in the equation above to get: $$Y_{3}=3,700+300(3)$$$$Y_{3}=3,700+900$$$$Y_{3}=4,600$$

Therefore, the forecast for October of this year is $4,600. The linear trend equation to predict monthly receipts is given by: $$Y_{t}=3,700+300t$$ where Y is the predicted monthly receipt and t is the time period in months where t=0 is July this year. The answer to the given question is: The forecast for October of this year is $4,600.

To know more about equation visit:

https://brainly.com/question/29657988

#SPJ11

Answer:

∠D

∠EDC

∠CDE

Step-by-step explanation:

those are the only ways I can think of, I hope that helps :)

(a) The probability distribution of the number of machines not running, and the mean of this distribution is 0.899.

(b)The expected fraction of time that the repair technician will be busy is 88.9% of the time.  

(a) Let X be the number of machines not running. At that point, X can take on values 0, 1, 2, 3, or 4. We will discover the likelihood conveyance of X as takes after:

P(X = 0) = P(all machines are running) = \(e^(-84)^4\)/4! = 0.302

P(X = 1) = P(one machine isn't running) = (4)(\(e^(-84)^3\)/3!) = 0.393

P(X = 2) = P(two machines are not running) = (6)(\(e^(-84)^2\)/2!) = 0.236

P(X = 3) = P(three machines are not running) = (4)(\(e^(-84)^1\)/1!) = 0.067

P(X = 4) = P(all machines are not running) = \(e^(-8*4)^0\)/0! = 0.002

The cruel(mean)  of this dispersion is E(X) = (0)(0.302) + (1)(0.393) + (2)(0.236) + (3)(0.067) + (4)(0.002) = 0.899.

(b) Let Y be the division of time that the repair specialist is active. At that point, Y can be communicated as

Y = T/(T + R),

where T is the full time that machines are not running

and R is the entire time that went through on repairs.

We know that

T has an Erlang dispersion with parameters

n = 4 and λ = 1/8 (since the running time of each machine has exponential dissemination with cruel 8 hours).

Subsequently, the anticipated esteem of T is E(T) = n/λ = 32 hours.

Additionally, R has an exponential dispersion with cruel 4 hours,

so E(R) = 4 hours. In this way, we have:

E(Y) = E(T/(T + R))

= E(T)/E(T + R)

= 32/(32 + 4)

= 0.889.

In this manner, ready to anticipate the repair professional to be active around 88.9% of the time. 

To know more about probability refer to this :

https://brainly.com/question/24756209

#SPJ4

Answer:

Step-by-step explanation:

Angle DBC is congruent with ADB as alternate interior angles

Answer:

1.05821886 ounces

Step-by-step explanation:

To convert 30 grams to ounces, use the conversion factor 1 ounce = 28.3495 grams.

Answer:

you know, you can't post more than one question

Step-by-step explanation:

Answer:

As Per Provided Information

A cylinder has a volume of 320 pi cubic inches and a height of 5 inches.

We have been asked to determine the radius of the cylinder .

Using Formulae

\( \purple{\boxed {\bf\: Volume_{(Cylinder)} = \pi {r}^{2}h}}\)

Substituting the value and let's solve for radius .

\( \sf \qquad \longrightarrow \: 320 \pi \: = \pi \: \times r {}^{2} \: \times 5 \\ \\ \\ \sf \qquad \longrightarrow \:320 \cancel{\pi} = \cancel{ \pi} \times r {}^{2} \: \times 5 \\ \\ \\ \sf \qquad \longrightarrow \:320 = r {}^{2} \: \times 5 \\ \\ \\ \sf \qquad \longrightarrow \:r {}^{2} \: = \cfrac{320}{5} \\ \\ \\ \sf \qquad \longrightarrow \: {r}^{2} = \cancel\cfrac{320}{5} \\ \\ \\ \sf \qquad \longrightarrow \: {r}^{2} = 64 \\ \\ \\ \sf \qquad \longrightarrow \:r \: = \sqrt{64} \\ \\ \\ \sf \qquad \longrightarrow \:r \: = 8 \: inch\)

Therefore,

Answer:

y = 4x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept, where it crosses the y- axis )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (- 2, - 4) ← 2 points on the line

m = \(\frac{-4-0}{-2-(-1)}\) = \(\frac{-4}{-2+1}\) = \(\frac{-4}{-1}\) = 4

the line crosses the y- axis at (0, 4 ) ⇒ c = 4

y = 4x + 4 ← equation of line

Answer:

38.6 units (nearest tenth)

Step-by-step explanation:

Formulae

(where r is the radius)

Circumference of a semicircle = diameter + half the circumference

⇒ Circumference of a semicircle = 2r + πr

Given:

\(\begin{aligned}\implies \textsf{Circumference of semicircle} & = 2(7.5) + \pi(7.5)\\ & = 15+7.5 \pi\\ & = 38.5619449...\\ & = 38.6\:\sf units\:(nearest\:tenth)\end{aligned}\)

Circumference

The number of people expected to have pretzels as their favorite snack is given as follows:

264 people.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The sample size is given as follows:

28 + 21 + 62 + 64 = 175.

The probability of a person having pretzels as their favorite snack is given as follows:

p = 21/175.

Hence the expected amount out of 2200 people is given as follows:

E(X) = 2200 x 21/175

E(X) = 264 people.

The results are given by the image presented at the end of the answer.

More can be learned about probability at https://brainly.com/question/24756209

#SPJ1

Answer:

2(a+b)

Step-by-step explanation:

Answer:

The half-life of carbon-14 is 5,730 years. This means that every 5,730 years, half of the carbon-14 in a sample will decay. So, if a sample contains 32% of its original amount of carbon-14, it is about 2 * 5,730 = 11,460 years old.

However, it is essential to note that radiocarbon dating is not an exact science. There is a margin of error of about 20 years. So, the skull's actual age could be between 11,260 and 11,660 years old.

Here is a formula that can be used to calculate the age of a sample using radiocarbon dating:

```

Age = (5,730 * ln(A/Ao)) / ln(2)

```

Where:

* Age is the age of the sample in years

* A is the amount of carbon-14 in the sample

* Ao is the original amount of carbon-14 in the sample

* ln is the natural logarithm function

In this case, A = 0.32 and Ao = 1.0. So, the age of the skull is:

```

Age = (5,730 * ln(0.32) / ln(2)) = 11,460 years

```

Step-by-step explanation:

Answer:

4535 years.

Step-by-step explanation:

The formula used to calculate the age of a sample by carbon-14 dating is3:

t=−0.693ln(N0​Nf​​)​×t1/2​

where:

t is the age of the sample

Nf is the number of carbon-14 atoms in the sample after time t

N0 is the number of carbon-14 atoms in the original sample

t1/2 is the half-life of carbon-14 (5730 years)

In your case, the skull contains 32% of its original amount of carbon-14, which means that Nf/N0 = 0.32. You can plug in this value and the half-life into the formula and get:

t=−0.693ln(10.32​)​×5730

Using a calculator, you can simplify this expression and get:

t=−1.139×−0.693×5730

t=4534.7

The maximum height of the road which is made in such a way that the center of the road is higher off the ground than the sides of the road is 16 feet.

The maxima of a parabola is where, it opens down its vertex at the maximum point in a coordinate graph. By equating the derivative of equation of parabola equal to zero, it can be found out.

A road is made in such a way that the center of the road is higher off the ground than the sides of the road, in order to allow rainwater to drain.

A cross-section of the road can be represented on a graph using the function,

\(f(x) = (x - 16)(x+ 16),\)

Here, x represents the distance from the center of the road, in feet.

This equation can be written as,

\(f(x) = (x - 16)^2\)

Now to find the maximum height, find the derivative of the above function as,

\(f(x) = (x - 16)^2\\f'(x) = (x - 16)^2\\f'(x)=2(x-16)(1)\\f'(x)=2(x-16)\)

Equate the above equation to zero as,

\(0=2(x-16)\\0=x-16\\x=16\)

Thus, the maximum height of the road which is made in such a way that the center of the road is higher off the ground than the sides of the road is 16 feet.

Learn more about the maxima of parabola here;

https://brainly.com/question/5399857