How many -digit even numbers are possible the digit cannot be zero?

Evaluate the value of expression.

So answer is 1.

Give the radius of a circle, r, we can find its area by using:

In the picture, the 30 ft segment passes from on side of the circle to the other passing thourhg tht center, so it is the diameter. The radius is half the diameter, so:

Now, we can use the formula for the area to find it:

So, the area is approximately 706.9 ft².

(a) The capacity of the tank is its volume, which we can calculate by multipling its sides:

This is, 168000 cm³. It is equivalent to 168 L.

(b) If the tank is being filled at a rate of 8 liters per minute, we can find the time to fill ir by dividing its capacity by the rate:

That is, it will take 21 minutos to fill it up.

SOLUTION:

Step 1:

In question 12, we are meant to find the line of reflection for Triangle ABC and its image based on the diagram:

Step 2:

The line of reflection for Triangle ABC and its image is:

EXPLANATION

The value of the number in the hundreths place is 0.07

You have the following expression:

"the sum of five squared and five"

the previous statement, in a mathematical form is:

5² + 5

It is important to point out that you have "the sum" of two numbers, which numbers? five squared and five.

The simplified form is:

5² + 5 = 25 + 5 = 30

She has already 500

x hours woked

pund we got:

7.50 x >= 900

And inequality could be

fx:o

because we need to gain 1400 or more

hours in order to have enough money to buy the computer

Sara needs to work at least 52 00/17.5

x >= 5r t o

The equatu

1

And then we can solve for x a

500+17.5x>>= 1400

utioen x

For this50 case we can do this:

500+ 17.

"S is the midpoint of BT": this is given.

BO || AT: this is given.

SB = ST: definition of midpoint.

alternate interior

vertical

ΔBOS = ΔTAS: SAS or ASA (both are right).

The general formula for a quadratic equation is ax² + bx + c = 0.

To solve

You can follow the steps.

Step 01: Write the equation in the general formula.

To do it, add 3 to each side of the equation.

Step 02: Use the Bhaskara formula to find the roots.

The Bhaskara formula is:

In this question,

a = 2

b = 6

c = 2

So, substituting the values:

Answer:

Exact form:

Decimal form:

Slope formula:

Replacing:

since x is constant , it is a vertical line, with an undefined slope.

Given in the question:

a.) There are four Defenders on a soccer team.

b.) This represents 20% of the players on the team.

you would have to do this backwards

20 times 2 would remove the /2

5c=40

40 divided by 5

is

8

C=8

y = 0.34x - 0.9 (Option A)

We are given the data and we want to find the line of best fit.

The line of best fit is a line that goes through the data points and it gives the best representation of the spread of the data.

The equation of a line is given as:

y = mx + c

y represents y-values

x represents x-values

m is the slope of the line

c is the y-intercept of the line or where the line crosses the y-axis.

To get this equation for this question, we need to find both m and c.

In order to do this, the formulas are given below:

While for c or the y-intercept, we have:

Before we can calculate m and c, we need to calculate the means of both x and y values give to us.

This is done below:

Now we can proceed to get the slope m of our line.

In order to be tidy, we shall use a table to solve. This table is shown in the image below:

Thus, we can now calculate our slope m:

Therefore the slope (m) = 0.34

Now to calculate intercept (c)

Therefore, the intercept (c) = - 0.9

Bringing it all together, we can write the equation of the line as:

y = 0.34x - 0.9

Therefore the answer is: y = 0.34x - 0.9 (Option A)

The number of pennies they lose altogether is 288 pennies.

Together, Katya and Mimi have 480 pennies in their piggy banks.

Therefore, there total amount of pennies is 480.

After Katya loses 1/2 of her pennies and Mimi loses 2/3 of her pennies, they have an equal number of pennies left.

Therefore,

let

x = number of pennies Katya have

y = number of pennies Mimi have

Hence,

x + y = 480

x = 480

Katya pennies left = x - 1 / 2x = 1 / 2x

Mimi pennies left = y - 2 / 3 y = 1 / 3 y

1 / 2 x  = 1 / 3 y

2y = 3x

y = 3  / 2 x

Substitute the value in equation(i)

x + 3 / 2 x  = 480

2.5x = 480

x = 480 / 2.5

x = 192

Therefore,

192 + y = 480

y = 480 - 192

y = 288

The number of pennies they loose can be calculated as follows;

Therefore, they lost 96 + 192 = 288 pennies altogether.

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From the given circle, the measure of the arc or the central angle indicated is as shown at the center of the circle is subtended by the arc

Hence, the measure of the arc or central angle indicated is 65° ,Option B

The average number of persons admitted in one year is X/5.

What is average number?

Average By adding a collection of numbers, dividing by their count, and then summing the results, the arithmetic mean is determined.

If X persons are admitted in last 5 years in a hospital.

Then we get the average value of admitted persons are X/5 per year.

If Y persons are recovered in last 5 years in a hospital.

Then we get the average value of recovered persons are Y/5 per year.

Therefore, the average number of persons admitted in one year is X/5.

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0.3821,  0.8745

========================================================

Work Shown:

pi/2 = 3.14/2 = 1.57 approximately

The solutions for t must be in the interval 0 ≤ t ≤ 1.57

[tex]3\cos(5t)+3 = 2\\\\3\cos(5t) = 2-3\\\\3\cos(5t) = -1\\\\\cos(5t) = -1/3\\\\5t = \cos^{-1}(-1/3)\\\\5t \approx 1.9106+2\pi n \ \text{ or } \ 5t \approx -1.9106+2\pi n\\\\t \approx \frac{1.9106+2\pi n}{5} \ \text{ or } \ t \approx \frac{-1.9106+2\pi n}{5}\\\\[/tex]

where n is an integer.

Let

[tex]P = \frac{1.9106+2\pi n}{5}\\\\Q = \frac{-1.9106+2\pi n}{5}\\\\[/tex]

Then let's generate a small table of values like so

[tex]\begin{array}{|c|c|c|} \cline{1-3}n & P & Q\\\cline{1-3}-1 & -0.8745 & -1.6388\\\cline{1-3}0 & **0.3821** & -0.3821\\\cline{1-3}1 & 1.6388 & **0.8745**\\\cline{1-3}2 & 2.8954 & 2.1312\\\cline{1-3}\end{array}[/tex]

The terms with surrounding double stars represent items in the interval 0 ≤ t ≤ 1.57

Therefore, we end up with the solutions 0.3821 and 0.8745 both of which are approximate.

You can use a graphing tool like Desmos or GeoGebra to verify the solutions. Be sure to restrict the domain to 0 ≤ t ≤ 1.57

Answer:

[tex]\textsf{c)} \quad 0.3821, \; 0.8745[/tex]

Step-by-step explanation:

Given equation:

[tex]3 \cos (5t)+3=2, \quad \quad 0\leq t\leq \dfrac{\pi}{2}[/tex]

Rearrange the equation to isolate cos(5t):

[tex]\begin{aligned}\implies 3 \cos(5t)+3&=2\\3 \cos(5t)&=-1\\\cos(5t)&=-\dfrac{1}{3}\end{aligned}[/tex]

Take the inverse cosine of both sides:

[tex]\implies 5t=\cos^{-1}\left(-\dfrac{1}{3}\right)[/tex]

[tex]\implies 5t=1.91063..., -1.91063...[/tex]

As the cosine graph repeats every 2π radians, add 2πn to the answers:

[tex]\implies 5t=1.91063...+2\pi n, -1.91063...+2 \pi n[/tex]

Divide both sides by 5:

[tex]\implies t=0.38212...+\dfrac{2}{5}\pi n,\;\; -0.38212...+\dfrac{2}{5} \pi n[/tex]

The given interval is:

[tex]0\leq t\leq \dfrac{\pi}{2}\implies0\leq t\leq 1.57079...[/tex]

Therefore, the solutions to the equation in the given interval are:

[tex]\implies t=0.3821, \; 0.8745[/tex]

1) Considering the Revenue function in the standard form:

2) Since this is a quadratic function, we can write out the Vertex of this function:

3) So, we can answer this way:

Area overall is 392 square metres. The two lawns' combined area is therefore 392 square metres.

A square is a quadrilateral in geometry that has four equal sides and four right angles (90-degree angles). It is a unique kind of both a rhombus and a rectangle. A square is made up of four equal-length sides, two equal-length diagonals, and right-angle diagonal cuts. A square's area and perimeter can be calculated by multiplying one of its sides by itself (squared), and one of its sides by four, respectively. Because of their symmetry and regularity, squares are frequently employed in mathematics and building.

given

By multiplying the first lawn's length by its breadth, one may determine its area: 56 square metres is the size of the first lawn, which is 8 metres by 7 metres.

The second lawn's breadth is six times that of the first lawn's, so:

The second lawn's width is equal to 6 × 7 metres, or 42 metres.

The second lawn is the same length as the first one, so:

The second lawn is 8 metres long.

The second lawn's area is calculated by multiplying its length by its width:

The second lawn is 336 square metres in size (8 metres by 42 metres).

The first and second lawns' combined areas make up the overall area of the two lawns:

Total area equals the sum of the first and second lawns.

56 square metres + 336 square metres make up the total area.

Area overall is 392 square metres. The two lawns' combined area is therefore 392 square metres.

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Given that a sugar sweet company costs to transport its sugar, 7500 to rent truck and additional 225 for each ton.

Statement Problem: Mr. Bensoua buys 3 bags of Flaming Hot Cheetos for every 4 bags of Takis. He buys a total of 14 bags of chips. If the Flamin Hot Cheetos cost $2 per bag and the Takis cost $2.50 per bag, how much did Mr. Bensoua spend on all of the chips?

Solution:

When Mr. Bensoua buys 4 bags of Takis, he buys 3 bags of Flaming Hot Cheetos.

When he buys another 4 bags of Takis, he buys 3 bags of Flaming Hot Cheetos.

At the end, he buys 8 bags of Takis and 6 bags of Flaming Hot Cheetos and that makes it a total of 14 bags of chips.

The cost of Takis per bag is $2.50, the cost of 8 bags of Takis is;

The cost of Flaming Hot Cheetos per bag is $2., the cost of 6 bags of Takis is;

Hence, the total amount Mr. Bensoua spends is;

CORRECT ANSWER: $32

Given the expression (-x + 2y - 3z)², we are to expand it using a suitable identity.

Using the square of the sum of trinomial identity expressed as:

From the given expression;

Substitute the parameters into the identity to expand as shown:

Simplify the result to have:

This gives the correct expansion using a suitable identity

Natural numbers are just counting numbers. It doesn't include a negative number. Integers include both positive and negative whole numbers. rational numbers are fractions that can be expressed as two integers. We can have - 8/1 = - 8

Finally, real numbers is any positive or negative number. It includes integers and rational numbers. Therefore, the subset that contains - 8 would be

real, rational and integer numbers

A line segment has the endpoints at (-6, -10) and (23, 6) then the midpoints of the line segment will be (17, -2).

An area or portion of a line with two endpoints is called a line segment. A line segment, in contrast to a line, has a known length. A line segment's length can be estimated by utilizing either metric measurements like millimeters or centimeters, or conventional measurements like feet or inches.

A line segment has the endpoints at (-6, -10) and (23, 6).

Mid point of the line segment is given by [tex]$\left(\frac{x_1+x_2}{2}\right),\left(\frac{y_1+y_2}{2}\right)$[/tex]

The midpoints of the line segment will be

=  [tex]$\frac{23+-6}{2}[/tex], [tex]$\frac{-10+6}{2}}[/tex]

= 17, -2

Therefore midpoints of the line segment will be (17, -2).

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First we dra a triangle:

To prove that the triangles are similar we have to do the following:

Considet triangles ABC and ACD, in this case we notice that angles ACB and ADC are equal to 90°, hence they are congruent. Furthermore angles CAD and CAB are also congruent, this means that the remaining angle in both triangles will also be congruent, therefore by the AA postulate for similarity we conclude that:

Now consider triangles ABC and BCD, in this case we notice that angles ACB and BDC are congruent since they are both equal to 90°. Furthermore angles ABC and DBC are also congruent, this means that the remaining angle in both triangles will, once again, be congruent. Hence by the AA postulate we conclude that:

With this we conclude that traingles BCD and ACD are both similar to triangle ABC, and by the transitivity property of similarity we conclude that:

Now that we know that both triangles are similar we can use the following proportion:

this comes from the fact that the ratios should be the same in similar triangles.

From this equation we can find h:

Plugging the values we have for x and y we have that h (that is the segment CD) has length:

Therefore, the length of segment CD is:

To solve this problem, we will first find the standard form of the circle equation. Given a circle of radius r and center (h,k), the standard form of the circle equation would be

In our case, we have h=8 , k=6 and r=10. So the equation for the given circle would be

The general form of the circle equation can be obtained from expanding the squares on the left side of the equality sign. Recall that

So, applying this to the standard equation we get

So our equation becomes

Operating on the left side, we have

By subtracting 100 on both sides, we get

which the general form of the equation of the given circle.

Using a graphing tool, we have that the circle's graph would be

From the given figures in the 2 triangles XYZ and ABC

mXZ = AC

m

Since we have two equal angles and the sides between them are equal, then

The 2 triangles are congruent using ASA postulate

The answer is C

Question:

There are 9.75 ounces of Cinnamon Toast Crunch in a bowl. Additional cereal is poured into the bowl at a rate of 1.5 ounces per second. How many ounces are in the bowl after 3 seconds?

Solution:

If additional cereal is poured into the bowl at a rate of 1.5 ounces per second, then in 3 seconds the additional cereal into the bowl is 1.5x 3 = 4.5 ounces. Thus after 3 seconds, the bowl has the original amount that it already had and the new aggregate:

9.75 ounces + 4.5 ounces = 14.25

then, the correct answer is:

14.25

To convert decimal numbers to percentage, what we need to do is to multiply the decimal number by 100, and we will get the representation as a percentage.

In this case we have the decimal number:

We multiply that number by 100 to write is as a percentage:

Answer: 75.1%