Thomas swims 10km each week during swim club. how many meters does he swim in 5 weeks​

Answer:

Step-by-step explanation:

36

Answer:

Step-by-step explanation: Multiplication first 7x1 = 7, Take 7 and divide it by 10 which gives you 0.7, Do the same but for the other 2 questions,

(9x1/100 = 0.09)

(9x1/1000 = 0.009)

(7x1/10 = 0.7)

Now take the answers and add them up

0.09 + 0.009 + 0.7 = 0.799

Answer: 0.799

Answer:

12

Step by step explanation

radius of a cone= square root of 3v

πh

r= square root of 3×2712.96

3.14×18

r= square root of 8138.88

56.52

r= square root of 144

r=12

The expression for the difference of two linear functions is (f - g)(x) = 4x - 6.

A linear function is a type of function in mathematics that has the form f(x) = mx + b, where x is the independent variable, f(x) is the dependent variable, m is the slope of the line, and b is the y-intercept.

To find the expression for the difference of two linear functions, f(x) and g(x), denoted by (f - g)(x).

The expression for (f - g)(x) can be found by subtracting g(x) from f(x):

(f - g)(x) = f(x) - g(x)

Substituting the given functions f(x) = x - 2 and g(x) = -3x + 4, we get:

(f - g)(x) = f(x) - g(x)

= (x - 2) - (-3x + 4) [Substitute the given values of f(x) and g(x)]

= x - 2 + 3x - 4 [Distribute the negative sign in front of (-3x + 4)]

= 4x - 6 [Combine like terms]

Therefore, (f - g)(x) = 4x - 6.

Option D (-3x² - 2x - 8) is incorrect as it involves squaring a linear expression, which would result in a quadratic expression. Option A (which has no operation between 3 and 22) is not a valid expression. Option B (-3x - 8) and C (3x3x22 or 198) do not take into account the fact that each sundae can be made using one of 3 syrups and one of 3 candy toppings.

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The 6 steps for inferential statistics to test researchers question can be:

It is the branch of statistics that is concerned with obtaining information about a population from a sample of that population. It is used to make inferences, that is, draw conclusions and make predictions about the population based on the information obtained from the sample.

These assertions are based on hypothesis tests, confidence intervals and statistical models.

Therefore, the goal of inferential statistics is to make accurate and reliable statements about the population using limited sample information.

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The cylinder's volume is 245 cubic units as a result.

It is possible to determine how much material a cylinder can carry by using its volume, which is known as its capacity in geometry. Cubic measurements for a cylinder's volume include cm³, m³, in³, etc.

The formula V = r²h is used to determine the volume of a cylinder, where r is the radius of its circular base and h is the height between the bases' perpendicular centers.

As a result, if r = 7 units and x = 5 units, we can use the formulas below to get the cylinder's volume:

V = πr²h

V = π(7)²(5)

= 245 cubic units per volt

Consequently, the size of the cylinder 245 cubic units as a result.

Complete question given below:

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If r = 7 units and x = 5 units, then what is the volume of the cylinder(height=x)?

The volume of the cylinder is 245π cubic units.

The cylinder is a three-dimensional shape having a circular base. A cylinder can be seen as a set of circular disks that are stacked on one another.

The formula for the volume of a cylinder is:

V = πr²h

where r is the radius of the base, h is the height, and π is the mathematical constant pi (approximately equal to 3.14).

Substituting r = 7 units and h = 5 units into the formula, we get:

V = π(7)²(5)

V = π(49)(5)

V = 245π

Therefore, the volume of the cylinder is 245π cubic units. Note that the volume is an exact value in terms of π, and cannot be simplified further without a numerical approximation of π.

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Answer: The answer to

sinΘ = 7/7√2

cosΘ = 7/7√2

tanΘ = 7/7

cosecΘ = 7√2/7

secΘ = 7√2/7

cotΘ = 7/7

Step-by-step explanation:

The given triangle consists of three sides namely, hypotenuse, opposite and adjacent.

The value of the hypotenuse is 7√2 and the value of the adjacent is 7.

We will calculate the value of the adjacent.

By Pythagoras' theorem,  (hypotenuse)^2=(opposite)^2+(adjacent)^2

Putting the given values, (7√2)^2=(opposite)^2+(7)^2

                                         (opposite)^2=(7√2)^2-(7)^2

                                         (opposite)^2=98-49

                                         (opposite)^2=49

Therefore, the value of the opposite is 7.

Now, we can put the following values in the trigonometric table.

sinΘ = opposite/hypotenuse = 7/7√2

cosΘ = adjacent/hypotenuse = 7/7√2

tanΘ =  opposite/adjacent = 7/7

cosecΘ = hypotenuse/opposite = 7√2/7

secΘ = hypotenuse/adjacent = 7√2/7

cotΘ = adjacent/opposite = 7/7

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The length of the hypotenuse of a 45-45-90 triangle is √2x units.

To find the hypotenuse of a 45-45-90 triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse).

Let's denote the length of each leg of the triangle as "x". Since the triangle is isosceles, both legs are of equal length. Therefore, we can write:

Leg 1 = Leg 2 = x

To find the length of the hypotenuse (which we'll call "h"), we can use the Pythagorean theorem as follows:

x² + x² = h²

Simplifying this equation, we get:

2x² = h²

To solve for h, we need to take the square root of both sides of the equation:

√(2x²) = √(h²)

√2 * x = h

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The volume of cone as per given figure is 314cm³.

The following mathematical operation must be carried out in order to determine a cone's volume: V = Π(h/3)r². The surface area of the circular portion of a cone is simply πr2. The lateral face wrapping around this base is calculated as πrl, or if you aren't given the slant height, you can use the formula πr√(r2+h2).

To calculate the volume of a cone, we apply the following formula:

, where V = volume

h = height

r = radius

π = pi

(h = height of cone, r= radius of cone)

Given:

Height of cone = 12 cm

Radius of cone = 5 cm

Volume of cone, V =  3.14 * (12/3 )* 5* 5

= 3.14 * 20 * 5

= 3.14 * 100

= 314 cm³

Therefore, The volume of cone as per given figure is 314cm³.

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Answer:

Step-by-step explanation:

1 )

a) quotient of powers as dividing two powers with the same base, we subtract the exponents.

b) product of powers when you are multiplying two terms with the same base, you add their exponents

c) property of negative exponents. According to the rules of exponents, a negative exponent can be rewritten as the reciprocal of the base raised to the positive exponent.

2)

Yes, when raising a fraction to a power with parentheses, the same principles apply as when raising a fraction to a power without parentheses. When evaluating expressions with fractions and exponents, the order of operations, including parentheses, is followed. To re-write the expressions (1/3)^2 is = (1/9) and (1/3)^-2 is equal to 9 9*(1/9) is 1 which is the rule of the product of powers. then the same applies to the second expression

3)

[tex](-2.3^{2})^{6}[/tex]  power to a power rule

[tex](\frac{1}{4}) ^{3}[/tex] power of a quotient

[tex]6^{4}[/tex] power to a power rule

[tex]7^{-1}[/tex] product of powers

ps: please grade me appropriately if you need more help with problems I am glad to help and these stars mean a lot to me. make sure you study your exponent laws and all the best!

The mean score of the given three scores is approximately 26.6, which is not the mean score for all ninth graders in the city.

To find the mean score for all ninth graders in the city, we need more information than just three scores. Without additional data, we cannot accurately determine the mean score for all ninth graders in the city.

However, we can calculate the mean of the given scores to verify that it is not 79.7 as claimed by the PR manager:

Mean = (77 + 91 + 71) / 3 = 79.7/3 = 79.7 ÷ 3 ≈ 79.7/3 ≈ 26.6

So the mean score of the given three scores is approximately 26.6, which is not the mean score for all ninth graders in the city.

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Answer:

Both 2B and 2A are not similar.

Step-by-step explanation:

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

Let me be helpful!

Let's start with 2B. It is easier to understand the subject that way.

->for a triangle to be similar, it's angles and sides must be the same.

-2B's triangle shows that line TW got scaled by x2.2 (22/10)

-Line ZW got scaled by 1.18

-2b are not similar.

Now on it 2A!

- line JK got scaled by 0.75

- Line JL got scaled by 0.5

-they are not similar

Let me know if I am incorrect!

-A friendly 8th grader :)

Six semicircles lie in the interior of a regular hexagon with a side length of 2 so that the diameters of the semicircles coincide with the sides of the hexagon. The zone of the shaded locale is around 10.3923 square units.

 We will approach this problem by first finding the region of the hexagon and after that subtracting the zones of the six semicircles from it. The zone of a customary hexagon with side length 2 can be found utilizing the equation:

Region of hexagon = (3√3/2) x side[tex]^{2}[/tex]

Substituting the given esteem of side length, we get:

Area of hexagon = (3√3/2) x 2[tex]^{2}[/tex] = 6√3

The range of a crescent is half the region of the comparing circle. So, the zone of each crescent is:

Range of semicircle = 1/2 x π x radius[tex]^{2}[/tex] = 1/2 x π x 1^[tex]^{2}[/tex]= π/2

There are six semicircles, so the whole range of the semicircles is:

Add up to the zone of semicircles = 6 x π/2 = 3π At long last, able to find the zone of the shaded locale by subtracting the region of the semicircles from the range of the hexagon:

Zone of shaded locale = Range of hexagon - Add up to a range of semicircles

= 6√3 - 3π

≈ 10.3923 thus, the zone of the shaded locale is around 10.3923 square units. 

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The length of ST obtained using Pythagorean Theorem is about 13.2 units

Pythagorean Theorem states that the square of the length of the hypotenuse side of a right triangle is the sum of the square of the other two legs of the triangle.

The length of the segment [tex]\overline{PR}[/tex] = 18

[tex]\overline{RS}[/tex] = [tex]\overline{SP}[/tex] = 16 (Radial length of the same circle)

Triangle ΔSRP is an isosceles triangle, therefore, ∠SRP ≅ ∠SPR

[tex]\overline{ST}[/tex] ≅ [tex]\overline{ST}[/tex] (Reflexive property of congruence)

Triangles ΔRST and ΔPST are congruent by the Hypotenuse Leg, HL rule of congruent triangles

Therefore; RT ≅ PT

RT + PT = 18

RT + RT = 18

2 × RT = 18

RT = 18/2 = 9

RT = 9

Therefore, ST, can be obtained using Pythagoras Theorem as follows;

ST = √(16² - 9²) = 5·√7 ≈ 13.2

The length of the side ST is about 13.2 units long

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Answer:

D.

Step-by-step explanation:

By looking at them I feel like D. is the best option

Answer:

Step-by-step explanation:

The equation of the parabola in vertex form is y = (1/4)x² - 6.

To write the equation of the parabola in vertex form, we use the formula:

y = a(x-h)² + k

Where (h,k) is the vertex and "a" is a constant that determines the shape of the parabola.

Given that;

The vertex is (0,-6)

Hence:

h = 0 and k = -6.

We can substitute these values into the formula to get:

y = a(x-h)² + k

y = a(x - 0)² - 6

y = ax² - 6

Now we need to find the value of "a". We are also given that the parabola passes through the point (-6,3).

x = -6 and y = 3

We can substitute this point into the equation to get:

y = a(x - h)² + k

3 = a( - 6)² - 6

3 = 36a - 6

9 = 36a

a = 1/4

Now we know the value of "a", we can substitute it back into the equation we derived earlier:

y = ax² - 6

y = (1/4)x² - 6

Therefore, the equation in vertex form is y = y = (1/4)x² - 6.

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Thus, the correct order of the numbers from least to greatest: 6% < 1/2 < 0.6 < 6/5

In an ascending list, the item that is smallest, first, or oldest will be at the top:

Given number-

1\2, 0.6,6%,6\5

convert all numbers in its fraction form:

1\2 = 0.5

0.6 = 0.6

6% = 0.06

6\5 = 1.2

Order  from least to greatest: 0.06, 0.5, 0.6 1.2

Or,

Thus, the correct order of the numbers from least to greatest 6% < 1/2 < 0.6 < 6/5

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Answer: Looks pretty good :) !

The mass of water vapor (g) / mass of dry air (kg) is the humidity measure of  the mixing ratio

The mixing ratio is defined as the mass of water vapor in grams divided by the mass of dry air in kilograms in a mixture of air and water vapor. It is a useful parameter for meteorologists and atmospheric scientists to describe the amount of water vapor in the atmosphere, particularly in the upper atmosphere where the relative humidity may be very low.

Relative humidity is the ratio of the partial pressure of water vapor in the air to the equilibrium vapor pressure at a given temperature and pressure, expressed as a percentage. Vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases at a given temperature in a closed system. Absolute humidity is the mass of water vapor per unit volume of moist air.

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There are 36 ways to arrange the letters d, i, g, i, t so that the two i's are not next to each other.

To find the number of ways the letters d, i, g, i, t can be arranged so that the two i's are not next to each other, follow these steps:
Consider the four non-i letters: d, g, t.

There are 3! (3 factorial) ways to arrange these letters, which is equal to 3 x 2 x 1 = 6 ways.

Since we want to prevent the two i's from being next to each other, we can think of placing them in the "gaps" between the non-i letters.

There are 4 possible gaps for the i's to be placed: (i) d (i) g (i) t (i).
Since there are two i's, we need to choose 2 of the 4 gaps to place them in.

This can be done in 4C2 ways (combination), which is equal to 4! / (2! x (4-2)!) = 6 ways.
Multiply the number of ways to arrange the non-i letters (step 1) with the number of ways to place the i's (step 3): 6 x 6 = 36.

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There are 72 ways to arrange the letters d, i, g, i, t so that the two i's are not next to each other.

To arrange the letters d, g, i, t, and i so that the two i's are not next to each other, follow these steps:

Step 1: Treat the two i's as one entity for now (denoted as [i]). So, we have 4 entities: d, g, t, and [i].
Step 2: Arrange these 4 entities (d, g, t, and [i]) in any order. There are 4! (4 factorial) ways to do this, which is 4 x 3 x 2 x 1 = 24 ways.
Step 3: Now, we need to separate the two i's. There are 3 spaces between the other letters (d, g, and t) where we can place the second i.
For example: if the arrangement is d-[i]-g-t, the second i can be placed in any of the three spaces indicated by the dashes.
Step 4: For each of the 24 arrangements from Step 2, there are 3 possible ways to place the second i. So, the total number of arrangements is 24 x 3 = 72 ways.

Thus, there are 72 ways to arrange the letters d, i, g, i, t so that the two i's are not next to each other.

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Yes, we can determine the probability of one thing happening before another based on their expected time to occur.

A coin has two sides: one side ("heads") is side A and the other ("tails") is side B. A coin is tossed into the air and the question is what are the chances, the "probability" if you want it to land on side A. The probability of an event occurring describes the number of chances that the event occurred. The total probability of hitting A before B is the sum: P(A before B) = p + rp + r² + r³p + r⁴p + … = p[1 + r + r² + r³ + r⁴ + … ] and this determines the result. Thus, it is possible to determine the probability of one thing happening before another, based on their expected time to occur.

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The number of feet per second that the remote control car travels is: 5 ft/s

The formula to find the speed from distance and time is:

Speed = Distance/time

Now, we are given:

Time: t = 3/40 seconds

Distance = 3/8 ft

Thus:

Speed = (3/8)/(3/40)

Speed = (3/8) * (40/3)

Speed = 5 ft/s

Thus, that is the speed that the remote control car travels

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A greater standard deviation for scores on the first quiz than on the second quiz would state that the results were less consistent on the first quiz than on the second quiz.

The standard deviation of a data-set measures the consistency of the data-set, and the higher the standard deviation, the less consistent the data-set is.

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To measure a length of 10 meters without any measuring devices from 100 meters rope is fold the rope ten times and 10th fold of 100 m rope is equals to 10 m.

Total Length of rope = 100 meters

We need to measure a length of 10 meters without using any measuring devices. The ways that we can use to measure the required length includes only fold or manipulate the rope, but you cannot cut or mark it. Now, we use the division arithmetic operation to measure the length. The factors of 100 is written as 100 = 2×2× 5×5 = 10× 10

If we divide 100 by 10 then results 10 as quotient and 0 as remainder. So, the rope with length 100 meters is divided into 10 parts of 10 meters length of rope. But we cannot cut the rope, so folds the rope ten times ( i.e, first half -half then again half into half-half). Therefore, the last fold is measure of length 10 meters.

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Therefore , the solution of the given problem of area comes out to be  the pizza only occupies 0.24 square inches of the box's bottom.

The object's overall size can be determined by figuring out how much room would be required to completely enclose the object's exterior. When selecting an analogous item with a tubular form, the environment is taken into account. Anything's total dimensions are determined by its surface area. The amount of water that a cuboid can hold depends on the number of sides that link its four trapezoidal shapes.

Here,

Assume that the square box's side length is "s" inches.

The pizza's size is specified as 254.47 in2. The area of the pizza would be equal to the area of the square box because it fits tightly inside of it.

=> s² = 254.47

=> s = √(254.47)

=> s = 15.95 inches

If you round to two decimal places, the area of the square box minus the area of the pizza is equal to (15.95)2 - 254.47, or 0.24 in2.

Therefore, the pizza only occupies 0.24 square inches of the box's bottom.

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The probability that at least 10 of them support tuition-free college is 0.9838.

To answer this question, we will use the binomial distribution formula. Let p = 0.51 be the proportion of young Americans who support tuition-free college, and let n = 30 be the sample size.

The probability of at least 10 UConn students supporting tuition-free college is equal to the sum of the probabilities of 10 or more, 11 or more, 12 or more, ..., up to 30. We can use the normal approximation to the binomial distribution.

Using the normal approximation, we first calculate the mean and standard deviation of the binomial distribution:
mean = np = 30 * 0.51 = 15.3
standard deviation = sqrt(np(1-p)) = sqrt(30 * 0.51 * 0.49) = 2.46

We then standardize the variable X = number of UConn students who support tuition-free college:
Z = (X - mean) / standard deviation

Now we want to find the probability that X is greater than or equal to 10, which is equivalent to finding the probability that Z is greater than or equal to (10 - 15.3) / 2.46 = -2.14.

Using a standard normal table or calculator, we find that the probability of Z being greater than or equal to -2.14 is approximately 0.9838. Therefore, the probability of at least 10 UConn students supporting tuition-free college is approximately 0.9838.

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Thus, the value of x for the given output of the function f(x) = 1 is found as: x = -1.

A function is a mathematical construct that receives an input, processes it according to a rule, and then outputs the outcome.

Given that:

Put f(x) = 1 in the given function to find x.

f (x) = - 5x - 4

1 = - 5x - 4

Isolating the x

-5x = 1 + 4

-5x = 5

x = 5/ -5

x = -1

Thus, the value of x for the given output of the function f(x) = 1 is found as: x = -1.

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