0.4x+2.9=1.5 solve for x

Hence proved,[tex](ST)^2=(TU*TV)[/tex]for given figure.

A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly called a rectangle triangle, is a triangle in which one angle is a right angle, i.e., in which two sides are perpendicular. The relation between the sides and other angles of the right triangle is the basis for trigonometry.

In mathematics, the Pythagoras  theorem or  Pythagorean  theorem is a fundamental relation  in Euclidean geometry between the three sides  of a right triangle. It states that the area of the  square whose side is the hypotenuse is equal to  the sum of the areas of the squares on the other two sides.

Use Pythagoras theorem , in given figure

than we get ,

in ΔTSU,

[tex](TU)^2=(ST)^2+(SU)^2[/tex]......(I)

inΔTVS,

[tex](ST)^2=(TV)^2+(SV)^2[/tex]......(II)

inΔSVU,

[tex](SU)^2=(VU)^2+(VS)^2[/tex].....(III)

from (I),

[tex](TU)^2-(ST)^2=(SU)^2=(VU)^2+(VS)^2[/tex]....(IV)  {by (III)

according to figure,TU=TV +VU

∴ [tex](TV+VU)^2=(VU)^2+(VS)^2+(ST)^2=(VU)^2+(VS)^2+(TV)^2+(SV)^2[/tex]{by (II)

use the identity,is

[tex](a+b)^2=a^2+2ab+b^2\\(TV)^2+2(TV)*(VU)+(VU)^2=(VU)^2+2(SV)^2+(TV)^2[/tex]

after simplification,

⇒[tex](TV)*(VU)=(SV)^2[/tex]

according to figure,TU=TV +VU ⇒VU=TU-TV

[tex](TV)*(TU-TV)=(SV)^2\\(TV*TU)-(TV)^2=(SV)^2\\(TV*TU)-(TV)^2=(SV)^2\\(SV)^2+(TV)^2=(TV*TU)\\(ST)^2=(TV*TU) {by(II)\\ OR (ST)^2=(TU*TV)[/tex]

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The solution is, 5.4 × 10⁻³ is the number in scientific notation.

Given:

The signal from a certain satellite takes approximately 0.0054 seconds to reach earth.

we will write the number in a scientific notation

The scientific notation is the number that is between 1 and 9 multiplied by 10 raised to an exponent

So, the given number will be:

0.0054

=54/10000

=54/10 * 1/1000

=5.4 × 10⁻³

Hence, The solution is, 5.4 × 10⁻³ is the number in scientific notation.

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From shortest to longest is:  C. Marisol, Juan, Lucia, Jamal.

By comparing the lengths of the students' walks, it is possible to determine the correct order of the students based on their walks.

Marisol walks 0.62 miles, while Juan walks one mile. So Juan's walk isn't the most limited.

Lucia walks one mile, which is shorter than Jamal's walk of 0.78 miles but longer than Marisol's walk of 0.62 miles. Therefore, neither the shortest nor longest walk is Lucia's.

Therefore, Jamal and Marisol remain choices. The correct order, from shortest to longest, is as follows because Jamal's walk is longer than Marisol's:

C. Marisol, Juan, Lucia, Jamal.

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Line JN = line AE = 22ft

Line DC = Line LM = 17ft

Line KL = line BC = 12 ft

< D = <M = 158°

< K = <B = 135°

Two shapes are said to be congruent when they both have the same length size and same angle measurements.

From the given shapes, polygon ABCDE = JKLMN.

Therefore the corresponding angles and lengths is as follows:

Line JN = line AE = 22ft

Line DC = Line LM = 17ft

Line KL = line BC = 12 ft

< D = <M = 158°

< K = <B = 135°

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Answer: 10 lego sets

Step-by-step explanation: The equation is 10X, 10 dollars times the amount of legos he is buying,

The variability in the heights of the seventh graders is approximately 0.6 times the variability in the heights of the sixth graders.

The variability or dispersion of a set of data is measured by the mean absolute deviation (MAD). By averaging the absolute differences between each data point and the set mean, it is calculated. Because it is less impacted by high values or outliers, the MAD is a more reliable measure of variability than the standard deviation. The MAD is always a non-negative number and is stated in the same units as the data. Greater variability is indicated by a bigger MAD, whereas a smaller MAD suggests that the data points are more variable and are consequently closer to the mean. The MAD is frequently used to track process variation in descriptive statistics and quality control applications.

Given that, MAD for the sixth graders is 1.2 and the MAD for the seventh graders is 0.7.

To determine the relation of variability we take the ratio as:

0.7 / 1.2 ≈ 0.6

Hence, the variability in the heights of the seventh graders is approximately 0.6 times the variability in the heights of the sixth graders.

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The complete question is:

Answer:

Step-by-step explanation:

I think is x-1

It is because you need to find f(1) and the formula of x-1 when x is greater and equal to 1.

The solutions to the equation [tex]tan^2(x) = (sec^2(x) - 1)[/tex]are:

x = 2nπ or x = (2n+1) π/2, where n is an integer.

The power reducing formula for the tangent function is:

[tex]tan^2(x) = (sec^2(x) - 1)[/tex]

Therefore, we can rewrite the equation as:

[tex](sec^2(x) - 1) = 0[/tex]

Simplifying further, we get:

[tex]sec^2(x) = 1[/tex]

Taking the square root of both sides, we get:

sec(x) = ±1

Recall that secant is the reciprocal of cosine, so we can write:

cos(x) = ±1

The cosine function can only take values between -1 and 1, so the only possible solutions are:

cos(x) = 1, which implies x = 2nπ (where n is an integer)

or

cos(x) = -1, which implies x = (2n+1)π/2 (where n is an integer).

The power reducing formula is a trigonometric identity that allows you to express a trigonometric function of a higher power in terms of a trigonometric function of a lower power.

It is most commonly used for reducing the power of the sine and cosine functions.

The power reducing formula for cosine is:

[tex]cos^2(x) = (1 + cos(2x))/2[/tex]

The power reducing formula for sine is:

[tex]sin^2(x) = (1 - cos(2x))/2[/tex]

These formulas can be derived using the Pythagorean identity, which states that [tex]sin^2(x) + cos^2(x) = 1.[/tex]

By solving for either[tex]sin^2(x) or cos^2(x)[/tex] in terms of the other, and then using the double angle formula for cosine[tex](cos(2x) = cos^2(x) - sin^2(x)),[/tex] we can arrive at the power reducing formulas.

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Jessie will cover a distance of about 486 yards.

The distance that Jessie will ride around the circular track can be calculated as the circumference of the circle.

The formula for the circumference of a circle is:

C = 2πr

Where C is the circumference, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

In this case, the radius of the circle is 25.8 yards.

We can substitute that into the formula and simplify:

C = 2πr

C = 2 × 3.14 × (25.8)

C = 162.024 yds

Since the circumference of the circular track is approximately 162.024 yards.

If Jessie rides around the track 3 times, the total distance she will ride is:

3 × 162.024 = 486 yards.

Therefore, option D) 486 yards is the correct answer.

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The coordinates of point P are (6.4, 18, -12).

A coordinate of a point refers to a set of values that specify the position of that point in a particular reference system or coordinate system. Coordinates are used to uniquely identify the location of a point in a geometric space, such as a plane or a three-dimensional space.

According to the given information:

To find the coordinates of point P, we can use the concept of vector comparison. We are given that the ratio of vector AB to vector AP is 6:4.

Let's denote the coordinates of point P as (x, y, z).

Given:

AB vector = (10, 2, -6)

B coordinates = (4, 6, -8)

AB:AP = 6:4

We can calculate the coordinates of point P as follows:

Since AB:AP = 6:4, we can express this as a vector equation:

(10, 2, -6) / (x - 4, y - 6, z + 8) = 6/4

Now we can cross-multiply to get:

10 / (x - 4) = 6/4

2 / (y - 6) = 6/4

-6 / (z + 8) = 6/4

Simplifying further, we have:

10(x - 4) = 6 * 4

2(y - 6) = 6 * 4

-6(z + 8) = 6 * 4

Expanding the equations, we get:

10x - 40 = 24

2y - 12 = 24

-6z - 48 = 24

Solving these equations, we get:

10x = 64

2y = 36

-6z = 72

Dividing by the respective coefficients, we get:

x = 6.4

y = 18

z = -12

So, the coordinates of point P are (6.4, 18, -12).

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The possible number of letter arrangements of 15 letter with 5 a's, 5 b's and 5 c's have no a's in the first 5 letters, no b's in the next 5 letters and no c's in the last 5 letters are equal to 2252.

Total number of letters for arrangement are 15 in count. Arrangment of 5 A's, 5 B's and 5 C's have no A's in the first 5 letters, no B's in the next 5 letters and no C's in the last 5 letters. In other words, we say that the first five letters must be B's or C's, the next five letters must be C's or A's, and the last five letters must be A's or B's. If there are k number of B's in the first five letters, then there must be (5-k) C's in the first five letters, like that there must be k C's and (5 - k ) A's in the next five letters, and k A's and (5-k) B's in the last five letters. That is number of each letter in each group of five letters is determined completely by knowing the number of B's in the first 5 letters. The number of ways to arrange, 15 letters with this restriction is [tex]$\binom{5}{k}^3$[/tex](since there are [tex]$\binom{5}{k}$[/tex]

ways to arrange k B's and 5-k C's that is arrangements ( 1B + 4C , 2B+ 3C , 3B+2C, 4B+ 1C ),similarly for next five arrangements (1A + 4C , 2A+ 3C , 3A+2C, 4A+ 1C ), ( 1B + 4C , 2B+ 3A , 3B+2A, 4B+ 1A ) and ( 5B, 5C, 5A), ( 5C,5B,A). Thus, the final answer for arrangement is [tex]$\sum_{k=0}^{5}\binom{5}{k}^{3}$[/tex]

Solve the above bionomial expression,

[tex]= \binom{5}{0}^{3} + \binom{5}{1}^{3} + \binom{5}{2}^{3} + \binom{5}{4}^{3} + \binom{5}{5}^{3} \\ [/tex]

[tex]= (\frac{ 5!}{5! 0!})^{3} + (\frac{ 5!}{4! 1!})³ + (\frac{5!}{3! 2!})³ + (\frac{5!}{2! 3!})³ + (\frac{5!}{1! 4!})³ + (\frac{5!}{0! 5!})³ \\ [/tex]

= 1 + 5³ + 10³ + 10³ + 5³ + 1

= 2252

Hence, required value is 2252.

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Answer: 41/56

Step-by-step explanation:

first you would try to find a common denominator (or LCM) in this case, its 56 so the revised question is 48/56+7/56 because you have to change the numerator as well. if you subtract the numerators it is 41. so its 41/56. 41/56 is already in its simplest form, so the answer is 41/56

The values that are equivalent to the fraction -10/7 are -(-10/7) and -13/7 which makes options D and E correct.

Equivalent fractions are fractions that have different numerators and denominators, but represent the same amount or quantity. In other words, equivalent fractions are different ways of representing the same fraction.

-10/-7 = 10/7 {not equivalent to - 10/7}

-3 1/7 = -22/7 {not equivalent to - 10/7}

1 3/7 = 10/7 {not equivalent to - 10/7}

- -10/-7 = - (-10/-7) = - 10/7 {equivalent}

- 1 3/7 = - 10/7 {equivalent}

Therefore, the values that are equivalent to the fraction -10/7 are -(-10/7) and -13/7.

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Answer: Median is 5

Step-by-step explanation: To find the median, we first need to arrange the numbers in order from least to greatest:

0 0 3 7 10 27

The median is the middle number, or the average of the two middle numbers if there are an even number of values. In this case, there are 6 values, so the median is the average of the two middle numbers:

median = (3 + 7) / 2

median = 5

Therefore, the median of the given numbers is 5.

Based on the function f(x) = 3 - x², the value of f(-2) include the following: f(-2) = -1.

In Mathematics and Geometry, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair in tables or relations.

In Mathematics and Geometry, a domain is sometimes referred to as input value and it can be defined as the set of all real numbers for which a particular function is defined.

When the domain (input value) of the given function f(x) is -2, the output value (range) is given by;

f(x) = 3 - x²

f(x) = 3 - (-2)²

f(x) = 3 - 4

f(x) = -1

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Answer:

1) The image of the line has the same slope as the pre-image but a different y-intercept.

hope this helps ;)

Answer: Oy = 15.5x

Step-by-step explanation: Gas mileage refers to the quantity of miles driven per unit volume of gasoline, typically expressed as "miles per gallon." In the context of the present inquiry, the vehicle in question exhibited a capacity to traverse a distance of 310 miles subsequent to the utilization of 20 gallons of gasoline. Thus, it is possible to calculate the gas mileage through the division of the quantity of gas consumed by the distance elapsed, resulting in:

The fuel efficiency of a vehicle, represented by the metric of gas mileage, is typically calculated by the ratio of distance traveled in miles to the amount of fuel consumed in gallons. In the present case, the gas mileage is equivalent to the quotient of 310 miles by 20 gallons, resulting in an efficiency rating of 15.5 miles per gallon.

The area of the pentagon with an apothem of 10 units is approximately 353.55 square units.

Area = (Perimeter × Apothem) / 2

Central angle = 360° / 5 = 72°

To find the area of a regular pentagon with an apothem of 10 units, we can use the formula:

Area = (Perimeter × Apothem) / 2

Central angle = 360° / 5 = 72°

Now, consider the right triangle formed by half of a side, the apothem, and the radius. The angle between the apothem and the radius (half of the central angle) is:

Angle = 72° / 2 = 36°

In the right triangle, we have:

tan(36°) = (s/2) / 10

Solving for s:

s = 2 * 10 * tan(36°) ≈ 14.142 units (rounded)

Now that we have the length of one side, we can calculate the perimeter of the pentagon:

Perimeter = 5 * s ≈ 5 * 14.142 ≈ 70.710 units (rounded)

Finally, we can find the area of the pentagon using the formula:

Area = (Perimeter × Apothem) / 2

Area = (70.710 × 10) / 2

≈ 353.55 square units (rounded)

The area of the pentagon with an apothem of 10 units is approximately 353.55 square units.

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Angle m1 has a value of 113 degrees.

Angles that are vertical (opposite in a vertical direction) Vertical angles, also known as vertically opposite angles, are the opposing angles formed when two lines converge. Angles that are vertically opposite one another are always equal to one another.

Alternate interior angles are made when a transversal joins two coplanar lines. They can be found on the inner side of the parallel lines, but on their transverse sides. The transversal goes through the two coplanar lines at two separate points.

According to the statement, it is creating a pair of linear angles whose sum is 180.

m1 + 67° = 180°

m1 = 113°

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The density of the milk is 1031.25 kg/m³.

Density refers to the mass of a unit volume of a material substance.

Density (ρ) = mass (m) / volume (V)

Given:

Volume (V) = 320cm³ = 0.00032m³

Mass (m) = 330g = 0.33kg

The Density (ρ) of the milk wll be:

= 0.33kg / 0.00032m³

= 1031.25 kg/m³

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The Central Limit Theorem (CLT) is an important theorem in statistics because it serves as the foundation for various statistical techniques and analyses.

The CLT states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the population's original distribution, provided that the population has finite mean and variance.
Normality:

The CLT establishes the concept of normality, which is a critical assumption in numerous statistical tests such as the t-test, z-test, and ANOVA. By knowing that the sample means are normally distributed, we can apply these tests to make inferences about population parameters.
Simplification:

Due to the CLT, we can simplify complex statistical problems by using normal distributions instead of dealing with the original population distribution.

Calculations more manageable and allows us to utilize the standard normal distribution table.
Confidence intervals:

The CLT enables us to construct confidence intervals for population parameters such as the mean.

Essential in estimating unknown population parameters based on sample data and understanding the associated uncertainty.
Margin of error:

The theorem helps in determining the margin of error for estimates, allowing us to quantify the accuracy of our estimates and make better decisions based on data.
Large sample sizes:

The CLT is particularly relevant when dealing with large sample sizes, as the distribution of sample means becomes more normal, and we can apply various statistical techniques with greater confidence.
The Central Limit Theorem is important in statistics because it enables us to assume normality, simplify problems, construct confidence intervals, determine the margin of error, and apply various statistical techniques with greater confidence, especially when dealing with large sample sizes.

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The area of sector DEF is 15.09 square units

The formula for area of a sector is:

A = (θ/360) * πr²

Where θ is the angle subtended at the center and r is the radius of the circle.

In this case, DE is the radius.

Thus r = 6 cm and θ = 48°

Substituting:

A = (48/360) * π * 6²

A = (48/360) * (22/7) * 36

A = 15.09 square units

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Complete Question

Check image attached

We may infer from the box plots that Super Fast Food, with its smaller IQR, is better equipped to predict wait times than Burger Quick.answer is option (a).

When values are sorted in order of magnitude, the median, a measure of central tendency, is the middle value in the collection.

BX charts are a common approach to visually depict a distribution of data, such as wait times at a drive-through restaurant. The bx in a bx plot depicts the interquartile range (IQR), or the middle 50% of the data, with the bttm and tp of the bx standing in for the first quartile (25th percentile) and third quartile (75th percentile), respectively. A line inside the box represents the median, or the value that splits the data into equal halves.

Although the range, which is the difference between the data's highest and minimum values, can also be used as a consistency indicator, its accuracy is lower than that of the IQR due to its sensitivity to extreme values and outliers. In this instance, Burger Quick's range is 30 - 2 = 28 minutes, while Super Fast Food's range is 27 - 3 = 24 minutes. Despite the fact that the range for Super Fast Food is narrower, it is still unreliable as a measure of consistency since it is significantly impacted by the outlier at 27 minutes, which is considerably outside the range of the data.

We may therefore deduce from the box plots that Super Fast Food, due to its smaller IQR, is able to estimate their wait time more reliably than Burger Quick.

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The complete question is,

The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.

A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.

A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.

Which drive-thru is able to estimate their wait time more consistently and why?

Burger Quick, because it has a smaller IQR

Burger Quick, because it has a smaller range

Super Fast Food, because it has a smaller IQR

Super Fast Food, because it has a smaller range

Step-by-step explanation:

The option that has the better value is the loose sweets.

What is division?

Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations.

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Which pack has the better value?

Price per gram for the bag = £1.49 / 120 = £0.0124

Price per gram for the loose sweets = £0.89 / 100 = £0.0089

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The probability of exactly 1 Jack being selected is 4249900100/2598960 = 38.46%.

The total number of combinations of selecting 5 cards from a deck of 52 cards is 52C5 = 5251504948/120 = 2598960.

The probability of exactly 4 of the 5 cards being Aces is 48*100/2598960 = 0.0018%.

The probability of all 5 of the cards being Spades is 1287*100/2598960 = 0.0495%.

The probability of exactly 4 of the 5 cards being face cards is 49540100/2598960 = 0.7618%.

The probability of exactly 2 Aces and exactly 2 Kings being selected is 1584*100/2598960 = 0.0609%.

The probability of exactly 1 Jack being selected is 4249900100/2598960 = 38.46%.

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Answer:

The annual percentage yield (APY) is a measure of the return on an investment that takes into account the effect of compounding interest. To calculate the APY for an investment of $8000 at an interest rate of 4.75% compounded daily, you can use the formula:

APY = (1 + r/n)^(n*t) - 1

where r is the annual interest rate as a decimal (0.0475 in this case), n is the number of times the interest is compounded per year (365 for daily compounding), and t is the number of years (1 in this case).

Plugging these values into the formula gives:

APY = (1 + 0.0475/365)^(365*1) - 1 APY ≈ 0.0486

So, the APY for this investment is approximately 4.86%.

Step-by-step explanation:

The possible rational zeros of the polynomial function are

±1, ±3, ±9, ±1/2, ±3/2, ±9/2

We have,

To find the possible rational zeros of the polynomial function P(x), we can use the Rational Root Theorem.

According to the theorem,

Any rational zero of a polynomial function with integer coefficients must have the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

In this case,

The constant term is -9, which has factors of ±1, ±3, ±9.

The leading coefficient is 2, which has factors of ±1, ±2.

So the possible rational zeros are:

±1/1, ±3/1, ±9/1, ±1/2, ±3/2, ±9/2

Simplifying the fractions, the possible rational zeros are:

±1, ±3, ±9, ±1/2, ±3/2, ±9/2

Thus,

The possible rational zeros are ±1, ±3, ±9, ±1/2, ±3/2, ±9/2

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