Using no digits other than 5 and 8, make a 6-digit number, that has the properties below. If it is impossible, write so. Of course you may use each digit more than once. c A multiple of 5, but not a multiple of 15.

Answer:

x = 79

Step-by-step explanation:

This is an isosecles triangle so the bottom angles have equal measure

and since the sum of interior angles in a triangle is equal to 180

2x + 32 = 180 subtract 32 from both sides

2x = 158 divide both sides by 2

x = 79

A bar chart or a histogram are visual representations of data that can be used to explore a single column of data.

A bar chart is used to compare different categories of data, and a histogram is used to measure the frequency of data within a given range. Bar charts allow a user to compare the differences between the categories of data, while histograms provide a better indication of how the data is distributed within the range.

Both bar charts and histograms are useful for identifying patterns, outliers, and trends in the data. By using a bar chart or a histogram, a user can quickly and easily identify where the data is concentrated, as well as identify any outliers or trends in the data.

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Statement  i. {a,b}∈{a,b,c,{a,b},R} is true. ii. {a,b}⊆{a,b,{a,b},R} is true. iii. {a,b}⊆P({a,b,{a,b},R}) is true. iv. {{a,b}}∈P({a,b,{a,b},R}) is true. v. {a,b,{a,b}}−{a,b}={a,b} is false. vi. AR+3=AR+1×A2 is true. vii. ∅∈∅×AR is false. viii. ∅=∅×∅ is true. R(A - B) ∪ (A - C) is a subset of A - (B ∩ C). Since both sides are subsets of each other, we can conclude that A - (B ∩ C.

i. True. The set {a, b} is an element of the set {a, b, c, {a, b}, R} since {a, b} is one of the elements in the set.

ii. True. The set {a, b} is a subset of the set {a, b, {a, b}, R} since all its elements, namely a and b, are also elements of the larger set.

iii. True. The set {a, b} is a subset of the power set of {a, b, {a, b}, R} since the power set of A includes all possible subsets of A, and {a, b} is one such subset.

iv. True. The set {{a, b}} is an element of the power set of {a, b, {a, b}, R} since the power set of A includes all possible subsets of A, and {{a, b}} is one such subset.

v. False. The set difference {a, b, {a, b}} - {a, b} is equal to {a, b, {a, b}}, not {a, b}.

vi. True. The expression AR+3 represents the Cartesian product of set A with itself twice, while AR+1 × A2 represents the Cartesian product of set A with itself once, followed by the Cartesian product of set A with itself again. These two expressions are equivalent.

vii. False. The empty set (∅) cannot be an element of any Cartesian product, including ∅ × AR. Cartesian products require at least one non-empty set as a factor.

viii. True. The empty set (∅) is equal to the Cartesian product of the empty set with itself, ∅ × ∅. Since there are no elements in either set, the Cartesian product is also empty.

(b) To prove A - (B ∩ C) = (A - B) ∪ (A - C), we need to show that both sides are subsets of each other.

First, let's show that A - (B ∩ C) is a subset of (A - B) ∪ (A - C):

Let x be an arbitrary element in A - (B ∩ C). This means that x is in A but not in B ∩ C.

If x is not in B, then x is in A - B, so (A - B) ∪ (A - C) contains x.

If x is not in C, then x is in A - C, so (A - B) ∪ (A - C) contains x.

Therefore, A - (B ∩ C) is a subset of (A - B) ∪ (A - C).

Next, let's show that (A - B) ∪ (A - C) is a subset of A - (B ∩ C):

Let x be an arbitrary element in (A - B) ∪ (A - C). This means that x is either in (A - B) or in (A - C).

If x is in (A - B), then x is in A but not in B. Since x is not in B ∩ C, it is in A - (B ∩ C).

If x is in (A - C), then x is in A but not in C. Since x is not in B ∩ C, it is in A - (B ∩ C).

Therefore, (A - B) ∪ (A - C) is a subset of A - (B ∩ C). Since both sides are subsets of each other, we can conclude that A - (B ∩ C.

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The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers. To calculate the t-value, the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

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The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

Given, M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers.

To calculate the t-value,

the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

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Answer:

\(y = {x}^{2} - 8x + 7 \\ a = 1 \: and \: b = - 8 \\ the \: line \: of \: symmetry \: \\ x = \frac{ - b}{2a} = \frac{8}{2} \\ x = 4(line \: of \: symmetry) \\ y = {4}^{2} - 8(4) + 7 \\ = 16 + 32 + 7 = y = 55 \\ vertix \: is \: (4 ,55) \\ y = {0}^{2} - 8(0) + 7 \\ y = 7 \\ 0 = {x}^{2} - 8x + 7 \\ (x - 7)(x - 1) = 0\)

The  probability of 6 successes in 7 independent trials with a probability of success 0.65 is 0.3052.

Using the binomial probability formula, the probability of x successes in n independent trials with a probability of success p can be calculated as:

P(x) = (n choose x) * p^x * (1-p)^(n-x)

where "n choose x" represents the number of ways to choose x items from a set of n items, and is calculated as:

(n choose x) = n! / (x! * (n-x)!)

So, for the given parameters nequals=7, pequals=0.65, xequals=6, we have:

P(6) = (7 choose 6) * 0.65^6 * (1-0.65)^(7-6)
     = 7 * 0.65^6 * 0.35^1
     = 0.3052

Therefore, the probability of 6 successes in 7 independent trials with a probability of success 0.65 is 0.3052.

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Answer:

The length of the banner is 24 inches and its width is 4 inches.

Step-by-step explanation:

Let the length of the banner be L.

Let the width of the banner be W.

The length is 6 times greater than the width. This means that:

L = 6W

The area of the banner is:

A = L * W = 6W * W = \(6W^2\)

The are of the banner is 96 square inches. This implies that:

\(6W^2\) = 96

=> \(W^2\) = 96 / 6 = 16

W = \(\sqrt{16}\)

W = 4 inches

The length, L, will be:

L = 6 * 4 = 24 inches

The length of the banner is 24 inches and its width is 4 inches.

6000FT, is the shortest length of fence that the rancher can use.

Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.

Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.

Imagine that your square is made up of smaller unit squares.

The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.

To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.

According to our question-

Let the rectangular field's length be x.

rectangle field width = y

square feet of a rectangular field's area

Because length is always positive, it is always positive.

Once more, discriminate with respect to x

replace x=1500

Therefore, at x=1 500, fencing is minimal.

Change x to 1 500.

the rectangular field is 1500 feet long.

rectangle field's width is 1000 feet.

Replace the values

shortest used fence length =6000ft

Hence, 6000FT, is the shortest length of fence that the rancher can use.

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Answer:

x= 108/61; y=-163/61

Step-by-step explanation:

(a) The hypothesis H: o > 110 asserts that the population parameter is greater than 110.

(b) The hypothesis H: X = 45 asserts that the sample statistic is equal to 45.

(c) The hypothesis H: S < 0.30 asserts that the sample statistic is less than 0.30.

(a) The assertion H: o > 110 is a legitimate statistical hypothesis because it is an assertion about the value of a parameter. The symbol o represents a population parameter, which is the true value of a characteristic of a population, such as the mean or the standard deviation.

The hypothesis H: o > 110 asserts that the population parameter is greater than 110. Therefore, this hypothesis can be tested using statistical methods, such as hypothesis testing or confidence intervals.

(b) The assertion H: X = 45 is a legitimate statistical hypothesis because it is an assertion about the value of a statistic. The symbol X represents a sample statistic, which is an estimate of a population parameter based on a sample of data.

The hypothesis H: X = 45 asserts that the sample statistic is equal to 45. Therefore, this hypothesis can be tested using statistical methods, such as hypothesis testing or confidence intervals.

(c) The assertion H: S < 0.30 is a legitimate statistical hypothesis because it is an assertion about the value of a statistic. The symbol S represents a sample statistic, which is an estimate of a population parameter based on a sample of data.

The hypothesis H: S < 0.30 asserts that the sample statistic is less than 0.30. Therefore, this hypothesis can be tested using statistical methods, such as hypothesis testing or confidence intervals.

In conclusion,whether an assertion is a legitimate statistical hypothesis depends on whether it is an assertion about the value of a parameter or a statistic, and whether there is enough information to test it using statistical methods.

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Answer:

Y=2

Step-by-step explanation:

YW thanks!

Answer:

Y= 1/7x + 2/7

Step-by-step explanation:

2/7 equals to b

Hope this helps.. :)

Answer:

x = 8

Step-by-step explanation:

x - 8/2 = 4

Follow your order of operations and divide first.

8/2 is 4

x- 4 = 4

Next, isolate the variable by using the additive property of equality.

x - 4 + 4 = 4 + 4

x = 8

Answer:

ok so u do the opposite of 8/2 so do 8*2 which is 16 then add the answer which is 4 which equals 20 so 20- 8/2=4, 20-16=4

Answer:

116/8 - 87/8 = 29/8 = 3 5/8 gal

Step-by-step explanation:

The answer is 50 grams of salt in the tank at all times.

To find the number of grams of salt in the tank at time t, we need to use the formula:

a(t) = a(0) + (r - p) * t

where a(0) is the initial amount of salt in the tank, r is the rate at which brine is being pumped into the tank, p is the rate at which the solution is being pumped out of the tank, and t is the time elapsed.

In this case, a(0) = 50 grams, r = 3 grams per minute (since the brine contains 1 gram of salt per liter and 3 liters are being pumped in per minute, so 3 grams of salt are being added per minute), and p = 3 grams per minute (since the solution is being pumped out at the same rate as it is being pumped in). Therefore, we can simplify the formula to:

a(t) = 50 + 0 * t
a(t) = 50 grams

This means that the amount of salt in the tank remains constant over time, since the rate at which it is being pumped in and out is equal. Therefore, the answer is 50 grams of salt in the tank at all times.

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Answer:

the total number of boxes being loaded is 1,200 trucks

Step-by-step explanation:

Given that

There are 48 boxes that should be loaded onto a truck

And, still it is required to lead 96% of the boxes onto the truck

We need to find out the total number of boxes that should be loaded

So

Since 48 boxes represent the 4% of the boxes that are loaded

So,

The total number of boxes would be

= 48 × 100 ÷ 0.04

= 1,200 trucks

Hence, the total number of boxes being loaded is 1,200 trucks

Answer:

The leading coefficient in the polynomial 10x2 + 3x - 5 is 10.

Step-by-step explanation:

To find the leading coefficient of the polynomial function, we must first locate the leading term. In a polynomial function, the leading term is the term containing the highest power of x. In this polynomial function, the leading term is 10x2. The leading coefficient of a polynomial function is the coefficient of the leading term, and so the leading coefficient of this polynomial function is 10.

Answer:

\(\angle BAC=180^{\circ}-\frac{13\sin 23^{\circ}}{6}\)

Step-by-step explanation:

\(\frac{\sin(\angle BAC)}{13}=\frac{\sin 23^{\circ}}{6} \\ \\ \sin \angle BAC=\frac{13\sin 23^{\circ}}{6} \\ \\ \angle BAC=180^{\circ}-\frac{13\sin 23^{\circ}}{6}\)

They would spend approximately 13.33 hours driving if they plan to cover a total distance of 800 miles at an average speed of 60mph.

To answer this question, we need to use the formula: time = distance/speed. In this case, the distance is 800 miles and the average speed is 60mph. Therefore, the time spent driving can be calculated as:
Time = 800 miles / 60 mph
Simplifying this equation, we get:
Time = 13.33 hours
So, the total time that they would spend driving is 13.33 hours. It's important to note that this is the average time it would take them if they maintained a constant speed of 60mph throughout their journey. However, if they encountered traffic, roadworks, or took any breaks during their trip, the actual time spent driving would be longer than this.
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Answer:

His time in minutes is 120

Step-by-step explanation:

(d)14/(r)7=(t)2 hours which equals 120 minutes

Answer:

120 minutes

Step-by-step explanation:

distance/speed=time

14/7mph=2 hours

2 hours = 120min

Answer:

Step-by-step explanation:

Distance between top of the tower and point of observation = 100 meters
Angle of Elevation = 45 degrees

Let's draw a right angle triangle with the following specifications.

tan(45 degrees) = x/100

tan(45 degrees) = 1

100(1) = x

x =  100 meters

The height of the tower is 100 meters.

The smallest positive angle measure in degrees is 30° and in radians it is π/6 radians (approximately 1.0472 radians).

This is because the coordinates (√3, 1) are on the terminal side of an angle in standard position and the angle is 30° from the positive x-axis.

This can be seen by drawing a right triangle with the coordinates (√3, 1) as the end point of the hypotenuse. The other two sides will have lengths of (1, 0) and (√3, -1). Using the Pythagorean theorem, we can calculate the length of the hypotenuse as 2.

The angle at the origin will be given by the ratio of the sides of the triangle, or arctan(√3/1). This can be simplified to arctan(√3), which is equal to 30° or π/6 radians.

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Answer:

Step-by-step explanation:

To factorize ,

6a+10ab

=2a(3+5b)    [ common 2a from both the terms]

For the given continuous random variable x:

(a) p(x < 4) = -8/27.

(b) p(3 ≤ x < 4) = -5/27

The continuous random variable x that can assume values between x = 2 and x = 5 has a density function given by f(x) = 2(1 x)/27.

(a) To find p(x < 4), we need to integrate the density function from x = 2 to x = 4:

p(x < 4) = ∫24 2(1 x)/27 dx

= (2/27) ∫24 (1 - x) dx

= (2/27) [(x - x2/2)]24

= (2/27) [(4 - 42/2) - (2 - 22/2)]

= (2/27) [(4 - 8) - (2 - 2)]

= (2/27) [(-4) - 0]

= (2/27) (-4)

= -8/27

So, p(x < 4) = -8/27.

(b) To find p(3 ≤ x < 4), we need to integrate the density function from x = 3 to x = 4:

p(3 ≤ x < 4) = ∫34 2(1 x)/27 dx

= (2/27) ∫34 (1 - x) dx

= (2/27) [(x - x2/2)]34

= (2/27) [(4 - 42/2) - (3 - 32/2)]

= (2/27) [(4 - 8) - (3 - 4.5)]

= (2/27) [(-4) - (-1.5)]

= (2/27) (-2.5)

= -5/27

So, p(3 ≤ x < 4) = -5/27.

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Answer:

false, a parallelogram does not have any lines of symmetry

Step-by-step explanation:

AB and YX are corresponding sides, BC and XZ are corresponding sides, and AC and YZ are corresponding sides of given triangle.

What is triangle?

A triangle is a two-dimensional geometric shape that has three sides, three angles, and three vertices. It is one of the simplest polygonal shapes and is commonly studied in geometry.

Since we have:

∠A ≅ ∠Y

∠B ≅ ∠X

∠C ≅ ∠Z

We can conclude that the two triangles ABC and XYZ are similar by the Angle-Angle (AA) similarity theorem.

Therefore, the corresponding sides of the two triangles are proportional to each other. We can write this as:

AB : YX = BC : XZ = AC : YZ

where AB and YX are corresponding sides, BC and XZ are corresponding sides, and AC and YZ are corresponding sides.

In other words, the ratio of the length of each side in triangle ABC to the corresponding side in triangle XYZ is constant.

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The required probability is 0.325 or 32.5%.

Event A and B are independent. Suppose P(B) = 0.4 and P(A and B) = 0.13.

Given: P(B) = 0.4P(A and B) = 0.13

Formula used: We know that when two events A and B are independent, then P(A and B) = P(A) × P(B)

Hence, the formula for finding P(A) can be given by:P(A) = P(A and B) / P(B)

Now, let's put the given values in the formula:P(A) = 0.13 / 0.4P(A) = 0.325

So, the probability of event A is 0.325 or 32.5% (approx).

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Answer:

x=1

Step-by-step explanation:

2+1+1+1+4=9

2+x+x+x+4=9

=> 3x + 6 = 9

=> 3x = 9-6

=> 3x = 3

=> x = 3/3

=> x = 1

✽ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ✽

➷  \(x + 3 = 21\)

➷ \(x = 21 - 3\)

➷ \(x = 18\)

✽

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ May ♡