Which of the following is NOT a true statement? There are 2 possible answers. Choose one.

A. ∠EFC measures 80°
B. ∠BFC & ∠DFE have a sum of 90°
C. ∠AFD measures 130°
D. ∠AFB& ∠CFD are supplementary

blank1 - Word Answer (-5,0)
blank2 - Word Answer (1,0)
blank3 - Word Answer (0,-5)

The x- and y-intercept(s) of an equation are the points where the graph of the equation crosses the x- and y-axis respectively. To find the x-intercept(s), we set y=0 and solve for x. To find the y-intercept, we set x=0 and solve for y.

a. x-intercepts:
0=(x+2)^2-9
9=(x+2)^2
±3=x+2
x=-5 or x=1
So the x-intercepts are (-5,0) and (1,0).

b. y-intercept:
y=(0+2)^2-9
y=4-9
y=-5
So the y-intercept is (0,-5).

Therefore, the correct answers are:
blank1 - Word Answer (-5,0)
blank2 - Word Answer (1,0)
blank3 - Word Answer (0,-5)

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Answer: 6 oz

Step by step:

5 < 6

Did i miss something?

Answer: 6 oz. is greater than 5 oz.

Step-by-step explanation:

Imagine you had 6 dogs. Now let's say that one passed away due to a car accident. Now you have 5 dogs. We can say by the fundamental theorem of common sense that you indeed did have more dogs before that accident. Using that logic in the grand scheme of metrics, we can say that 6oz is larger as a value than 5oz.

Answer:

60

Step-by-step explanation:

850-250=600

600/10=60

60

Answer:

she must save $60 each week to have enought money to purchase the iPhone 10

Step-by-step explanation:

Because 850-250=600

                 600/10=60                

If the dividend is 872 and the quotient is 62 and remainder is 4, the divisor is equal to 14.

In Mathematics, a quotient can be defined as a mathematical expression that is typically used for the representation of the division of a number by another number.

In Mathematics, dividend can be calculated by using this mathematical expression:

Dividend = divisor × quotient + residual

Substituting the given data points into the dividend formula, we have the following;

Dividend = divisor × quotient + residual

872 = divisor × 62 + 4

Divisor = (872 - 4)/62

Divisor = 868/62

Divisor = 14

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Complete Question;

If the dividend is 872 and the quotient is 62 and remainder is 4. What is the divisor?

The figure represented here is a square pyramid.

With a square base and fοur triangular sides that are cοnnected at a vertex, a square pyramid is a three-dimensiοnal geοmetric οbject. It has a pentahedrοn shape with five faces.

Fοur triangles are jοined at each vertex tο a square fοundatiοn tο fοrm a square pyramid. It has a square fοundatiοn, and triangles with a shared vertex make up its side faces.

We can get the squared pyramidal figure by fοlding the triangles οf equal size frοm all the sides.

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The required sinusoidal function be,

⇒ y = 25 sin(2π/15 (x - 1 + 15/4 + 30nπ)) + 38

                 or

⇒ y = 25 sin(2π/15 (x - 1 - 15/4 - 30nπ)) + 38

Since we know that,

The general formula of a sinusoidal function is,

⇒ y = A sin(B(x - C)) + D,

where,

A is the amplitude

B is the frequency (and related to the period by T = 2π/B)

C is the phase shift (the horizontal displacement from the origin)

D is the vertical shift (the midline)

Using the given information,

Amplitude = 25, so A = 25.

Period = 15, so T = 15.

We know that,

T = 2π/B, so we can solve for B,

⇒ 15 = 2π/B

⇒  B = 2π/15

Midline is y = 38, so D = 38.

⇒ f(1) = 63,

so we can also use this to find the phase shift:

⇒ 63 = 25 sin(B(1-C)) + 38

⇒ 25 sin(B(1-C)) = 25

⇒ sin(B(1-C)) = 1

⇒ B(1-C) = π/2 + 2nπ or 3π/2 + 2nπ,

where n is an integer.

Substituting B and solving for C in each case, we get,

⇒ B(1-C) = π/2 + 2nπ 2π/15 (1 - C)

              = π/2 + 2nπ 1 - C

              = 15/4 + 30nπ C

              = 1 - 15/4 - 30nπ

⇒ B(1-C) = 3π/2 + 2nπ 2π/15 (1 - C)

              = 3π/2 + 2nπ 1 - C

              = 15/4 + 60nπ/2 C

              = 1 - 15/4 - 30nπ

So we have two possible functions are,

⇒ y = 25 sin(2π/15 (x - 1 + 15/4 + 30nπ)) + 38

                 or

⇒ y = 25 sin(2π/15 (x - 1 - 15/4 - 30nπ)) + 38

where n is any integer.

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Answer:

Step-by-step explanation:

Let [tex]x[/tex] be number of $1 bills.

Let [tex]y[/tex] be the number of $5 bills.

So we get:

[tex]x+y=60[/tex]       [tex](1)[/tex]

[tex]x+5y=150[/tex]   [tex](2)[/tex]

Then we solve these simultaneously:

[tex](2)-(1)[/tex]  gives

[tex]4y=90[/tex]  ⇒ [tex]y=22.5[/tex]

Substitute [tex]y=22.5[/tex] into [tex](1)[/tex] gives:

[tex]x+22.5=60[/tex]  ⇒  [tex]x=37.5[/tex]

So there appears to be no solution to this question as you cannot have half bills.

If I understand your question correctly, pure water is 0% alcohol, so by adding water, this will dilute your 15% alcohol solution and lower the percentage of alcohol in the solution.

Many word problems are set up like "You have some amount of 15% alcohol solution and you add some pure water.  You end up with some other amount of the diluted mixture.  How much 15% alcohol solution and how much pure water were mixed."  

For those ones, use 0% alcohol for your pure water.

Tο depict the relatiοnship between twο numerical variables using Data visualizatiοn that is knοwn as a scatterplοt.

Using this scatterplοt, we graphed a line using linear regressiοn. This line can use as οur reference pοint and ignοre the rest οf the pοints οn the graph.

We will examine this graph and try tο find apprοximately what value οf y is given when we prοvide an x value.

Since the number οf hits is the x value, tο find hοw high the graph gοes at that x value we can lοοk at the graph tοο.

Right between 100 and 150 is 125, sο we can nοw start there and mοve up.

When we mοve up, we get a line that's between 10 and 20. We can alsο view it's in the tοp half οf that bοx. That means the value οf y fοr this will be mοre than 15.

Since it's nοt lying directly οn 20, we have the οnly οptiοn left is 18.

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To show that Col A is the subspace spanned by the columns of A, we need to show that:

Col A is a subspace of RN.

Col A is spanned by the columns of A.

To show that Col A is a subspace of RN, we need to show that it satisfies the three subspace properties:

a. Col A contains the zero vector. This is true since the equation Ax = 0 always has a solution x = 0, which means that the zero vector is in Col A.

b. Col A is closed under addition. Suppose b1 and b2 are in Col A, so there exist x1 and x2 such that Ax1 = b1 and Ax2 = b2. Then, for any scalars c1 and c2, we have:

A(c1x1 + c2x2) = c1Ax1 + c2Ax2 = c1b1 + c2b2

which shows that c1b1 + c2b2 is also in Col A.

c. Col A is closed under scalar multiplication. Suppose b is in Col A, so there exists x such that Ax = b. Then, for any scalar c, we have:

A(cx) = c(Ax) = cb

which shows that cb is also in Col A.

Therefore, Col A is a subspace of RN.

To show that Col A is spanned by the columns of A, we need to show that any vector b in Col A can be expressed as a linear combination of the columns of A. By definition, there exists an x such that Ax = b.

This means that b is a linear combination of the columns of A, with the coefficients given by the entries of x. Specifically, if A has columns a1, a2, ..., an, then:

b = Ax = x1a1 + x2a2 + ... + xn an

Therefore, Col A is spanned by the columns of A.

Overall, we have shown that Col A is the subspace spanned by the columns of A.

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The formula for calculating the effective annual rate of interest with quarterly compounding is:

(1 + r/4)^4 - 1 = A/P

where r is the quarterly interest rate, A is the final amount, and P is the principal.

In this case, P = $2,000, A = $3,000, and the time period is 7 years or 28 quarters.

So we have:

(1 + r/4)^4 - 1 = 3000/2000

(1 + r/4)^4 = 1.5

1 + r/4 = (1.5)^(1/4)

r/4 = (1.5)^(1/4) - 1

r = 4[(1.5)^(1/4) - 1]

To get the effective annual rate, we need to convert the quarterly rate to an annual rate by multiplying by 4:

effective annual rate = 4[(1.5)^(1/4) - 1] ≈ 8.84%

Therefore, the effective annual rate of interest at which $2,000 will grow to $3,000 in seven years if compounded quarterly is approximately 8.84%, rounded to 2 decimal places.

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The size of the angle that the line DE makes with the plane ABCD is 50.8 degrees

From the question, we have the following parameters that can be used in our computation:

The figure

To start with, we calculate the measure of length BE using the following tangent ratio

tan(60) = BE/60

So, we have

BE = 60√3

Next, we calculate DB using the Pythagoras theorem

DB = √(60² + 60²)

Evaluate

DB = 60√2

The measure of the required angle is then calculated as

tan(Angle) = 60√3/60√2

Evaluate

tan(Angle) = 1.2247

Take the arc tan

Angle = 50.8 degrees

Hence, the angle is 50.8 degrees

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The linear system shown is "inconsistent" in nature.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

The given figure is represented linear system represents two parallel lines.

Now, the solution set of the two system of equations could be find by finding their points of intersection.

And when the lines do not intersect then it is said the linear system of the two lines do not have any solution.

Now, we have been given two parallel lines and parallel lines never intersect each other. thus the solution set of both the system of equations represented by these parallel lines is an empty set.

And when the system of linear equation has no solution , then the system is said to be inconsistent.

Hence, The linear system shown is "inconsistent" in nature.

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The complete question is;

The linear system shown is _____.

independent

equivalent

inconsistent

The value of a is 20, b is 40, c is 10 and d is 10√3

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

By using sine function we find the value of a

sin 45=a/20√2

1/√2 = a/20√2

20√2=a√2

a=20

Now let us find c

cos 45=c/(20√2)

1/√2×20/√2=c

10=c

sin30=a/b

1/2=20/b

b=40

Now we have to find d by cosine function

cos30=d/a

√3/2=d/20

d=10√3

Hence, the value of a is 20, b is 40, c is 10 and d is 10√3

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The variance of the sample of data is 3.33.

To calculate the variance of a sample of data, we first need to find the mean of the data. The mean is the average of all the data points.

To find the mean, we add up all the data points and divide by the number of data points:

(7 + 5 + 8 + 4 + 6 + 3 + 9 + 7 + 6 + 5) / 10 = 60 / 10 = 6

Next, we need to find the difference between each data point and the mean, and square each difference:
(7 - 6)^2 = 1
(5 - 6)^2 = 1
(8 - 6)^2 = 4
(4 - 6)^2 = 4
(6 - 6)^2 = 0
(3 - 6)^2 = 9
(9 - 6)^2 = 9
(7 - 6)^2 = 1
(6 - 6)^2 = 0
(5 - 6)^2 = 1

Next, we add up all the squared differences:

1 + 1 + 4 + 4 + 0 + 9 + 9 + 1 + 0 + 1 = 30

Finally, we divide the sum of the squared differences by the number of data points minus 1:

30 / (10 - 1) = 30 / 9 = 3.33

Therefore, the variance of the sample of data is 3.33.

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The correct answer is c. Failed to reject the null hypothesis.

Failed to reject the null hypothesis.

Explanation:

In this problem, we are given the price of drugs for human doses and animal doses from different pharmacies. We are asked to form a statistical decision using the p-value method. The null hypothesis is that the prices for the animal doses are equal to the prices for the human doses, while the alternative hypothesis is that the prices for the animal doses are significantly less than the prices for the human doses.


To form a statistical decision, we need to compare the p-value with the level of significance (α). If the p-value is less than or equal to α, we reject the null hypothesis. If the p-value is greater than α, we fail to reject the null hypothesis.


In this case, the level of significance is 1% (α=0.01). Since the p-value is not given in the problem, we cannot make a decision. Therefore, the correct answer is c. Failed to reject the null hypothesis.

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The solutions to the equations are;

1) {-2, 1/2}

2) {0, -2}

The zero product property is a fundamental property of algebra that states that if the product of two or more factors is equal to zero, then at least one of the factors must be zero. In other words, if a × b = 0, then either a = 0, b = 0, or both a and b are equal to zero.

Using the zero product property;

2x - 1 = 0

x = 1/2

x + 2

x = -2

The solution is;

{-2, 1/2}

Again for x(x + 2) = 0

x = 0

x + 2 = 0

x = -2

The solution is;

{0, -2}

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Answer:

1.7 × .5 = .85

15% smaller than the original

Simplifying the expression (2x³ – 2x² – 40x )/(2x² + 5x - 12) ÷ (6x⁴ – 150x²)/(8x³ - 27) will result to (x - 5)/(3x(x - 3)(x + 5)).

To simplify the given expression completely, we need to factor the numerator and denominator of each fraction, and then simplify by canceling out common factors.

(2x³ – 2x² – 40x )/(2x² + 5x - 12) ÷ (6x⁴ – 150x²)/(8x³ - 27)

= (2x(x² - x - 20))/(2x^2 + 5x - 12) ÷ (6x^2(x^2 - 25))/(8x^3 - 27)

= (2x(x - 5)(x + 4))/(2x² + 8x - 3x - 12) ÷ (6x²(x - 5)(x + 5))/(8x³ - 27)

= (2x(x - 5)(x + 4))/(2x(x + 4)(x - 3)) ÷ (6x²(x - 5)(x + 5))/(8x³ - 27)

= (2x(x - 5)(x + 4))/(2x(x + 4)(x - 3)) × (8x³ - 27)/(6x²(x - 5)(x + 5))

= (x - 5)/(x - 3) × (8x³ - 27)/(6x²(x - 5)(x + 5))

= (x - 5)/(x - 3) × (2x - 3)(4x² + 6x + 9)/(6x²(x - 5)(x + 5))

= (x - 5)/(x - 3) × (2x - 3)/(6x(x - 5)(x + 5))

= (x - 5)/(3x(x - 3)(x + 5))

Therefore, the simplified expression is (x - 5)/(3x(x - 3)(x + 5)).

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Answer:

The pattern described in the question follows the rule that each consecutive line has a number that is one less than twice the previous line. Starting with 2 as the first line, the pattern can be written as follows:

1st line: 2

2nd line: 2(2) - 1 = 3

3rd line: 2(3) - 1 = 5

4th line: 2(5) - 1 = 9

5th line: 2(9) - 1 = 17

6th line: 2(x) - 1 (unknown)

To find the number of marbles in the 6th line, we can use the rule of the pattern and solve for x:

2(x) - 1 = 2(17) - 1 (substitute 17 for the number in the 5th line)

2x - 1 = 33

2x = 34

x = 17

Therefore, the 6th line of the pattern would have 17 marbles

Step-by-step explanation:

The pattern is described as having a number in each line that is one less than twice the previous line.

Write out the first few lines of the pattern, starting with 2 as the first line:

1st line: 2

2nd line: 2(2) - 1 = 3

3rd line: 2(3) - 1 = 5

4th line: 2(5) - 1 = 9

5th line: 2(9) - 1 = 17

To find the number of marbles in the 6th line, use the pattern rule and substitute the value for the 5th line:

6th line: 2(x) - 1

Substitute 17 for x (the value in the 5th line):

2(x) - 1 = 2(17) - 1

Simplify the right-hand side:

2(x) - 1 = 33

Add 1 to both sides:

2(x) = 34

Divide both sides by 2:

x = 17

Therefore, the 6th line of the pattern would have 17 marbles.

The complete pattern in the given question is: 2, 3, 5, 9, 17, 33.

To solve this problem, we need to apply the given rule to generate the numbers in the sequence and then find the sixth number.

Starting with two, we can apply the rule to generate the next few numbers:

First line: 2

Second line: 2(2) - 1 = 3

Third line: 2(3) - 1 = 5

Fourth line: 2(5) - 1 = 9

Fifth line: 2(9) - 1 = 17

Now we can apply the rule again to find the sixth number:

Sixth line: 2(17) - 1 = 33

Therefore, the sixth line must have 33 marbles.

The pattern starts with two, which is the first line.

The second line follows the given rule: "every consecutive line has a number that is one less than twice the previous line". We can apply this rule to the first line by multiplying it by 2 and subtracting 1: 2(2) - 1 = 3. Therefore, the second line has 3 marbles.

To find the third line, we can apply the same rule to the second line: 2(3) - 1 = 5. Therefore, the third line has 5 marbles.

Similarly, we can find the fourth line by applying the rule to the third line: 2(5) - 1 = 9. Therefore, the fourth line has 9 marbles.

We can find the fifth line by applying the rule to the fourth line: 2(9) - 1 = 17. Therefore, the fifth line has 17 marbles.

Finally, to find the sixth line, we apply the rule again to the fifth line: 2(17) - 1 = 33. Therefore, the sixth line has 33 marbles.

So, the complete pattern is: 2, 3, 5, 9, 17, 33.

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Using the definition of a parallelogram in Euclid's first book, we can say that a non-perpendicular, unequal, non-bisecting diagonal produces either a trapezium or a rhombus if the opposite angles are equal, then it is a rhombus, and if the opposite angles are unequal, then it is a trapezium.

To use Euclid's first book to prove what specific quadrilaterals are produced by non-perpendicular, unequal, non-bisecting diagonals, start by considering Euclid's definitions of a parallelogram, a trapezium, and a rhombus.

In Euclid's first book, a parallelogram is defined as a quadrilateral which has two pairs of equal and parallel sides, while a trapezium is defined as a quadrilateral which has two pairs of opposite sides parallel, but with the other two sides unequal and non-parallel.

Finally, a rhombus is defined as a quadrilateral (parallelogram) which has all four sides equal, and with the opposite angles equal.

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Answer:

To find the value of b x6 when b = 7, we simply need to substitute 7 for b in the expression and perform the multiplication.

b x 6 = 7 x 6

Multiplying 7 by 6 gives us:

b x 6 = 42

Therefore, when b = 7, the value of b x 6 is 42.

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7527861800

The state space is {0, 1, 2, 3},

The transition matrix is : P = [[(1-p)³, 3p(1-p², 3p²(1-p), p^3], [(1-p)², 2p(1-p)²+2p(1-p)², 2p²(1-p)+2p²(1-p), 2p³], [(1-p), p(1-p)²+2p(1-p), p²(1-p)+2p², p³], [0, p(1-p), 2p², 3p³]],  the probability of one idle machine 3 nights later is 0.33554432.

The state space of (Xn : n ≥ 0) is the set of all possible states that the system can be in at the end of a given day. The state space is {0, 1, 2, 3}, where 0 corresponds to all machines being broken, 1 corresponds to one machine working and two broken, 2 corresponds to two machines working and one broken, and 3 corresponds to all machines working.

The transition matrix is given by:
P = [[(1-p)³, 3p(1-p², 3p²(1-p), p^3], [(1-p)², 2p(1-p)²+2p(1-p)², 2p²(1-p)+2p²(1-p), 2p³], [(1-p), p(1-p)²+2p(1-p), p²(1-p)+2p², p³], [0, p(1-p), 2p², 3p³]]

Given that 2 machines are idle tonight (i.e., Xn = 1), the probability of one idle machine 3 nights later (i.e., Xn+3 = 2) is given by the (1, 2) entry of P^3, where P^3 is the matrix obtained by multiplying P by itself 3 times.

Using the given value of p = 0.8, we can calculate P^3 and find the (1, 2) entry to obtain the desired probability. The (1, 2) entry of P^3 is 0.33554432, so the probability of one idle machine 3 nights later is 0.33554432.

Therefore, the answer to part c is 0.335544.

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The first set is countable, the second set is also countable. The third set is also countable.

(a) The set {x∈R:2 is countable because it is finite.
(b) The set {x∈Q:∣x∣≥2} is countable because it is a subset of the rational numbers, which are countable.
(c) The set {x∈Q:∣x∣<4} is countable because it is a subset of the rational numbers, which are countable.

In Maths, sets are referred as a collection of well-defined objects or elements. A set is usually represented by a capital letter symbol and the total number of elements in the finite set is basically represented as the cardinal number of a set in a curly bracket.

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The combination that is produced contains 57.5% corn.. It is calculated by taking the weighted average of the corn content in the two bags, accounting for their respective weights.

(50% x 20 lbs) + (65% x 30 lbs)

= 1750 lbs + 1950 lbs

= 3700 lbs

3700 lbs/50 lbs

= 57.5%

The concentration of corn in the resulting mixture is 57.5%. This is calculated by taking the weighted average of the corn content in the two bags. The first bag, containing 20 pounds of calf starter mix, contains 50% corn. The second bag, containing 30 pounds, contains 65% corn. To calculate the concentration of corn in the mixture, the percentage of corn in each bag is multiplied by its respective weight, and the sums of these two products are then divided by the sum of the two weights. In this case, (50% x 20 lbs) + (65% x 30 lbs) = 1750 lbs + 1950 lbs = 3700 lbs. The resulting concentration of corn in the mixture is 3700 lbs/50 lbs = 57.5%.

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Answer:

[tex]\boxed{R:-40.48}[/tex]

Step-by-step explanation:

Rewriting the statement we have:

[tex]-44+22 \times\frac{ 16}{100}[/tex]

According to the order of operations, we solve:

simplify:

[tex]-44+22 \times\frac{ 4}{25}\\=-44 +\frac{88}{25} \\=\frac{-44(25)+88}{25} = \frac{-1012}{25} \approx -40.48[/tex]

To determine how much greater the fractional part of a college student's daily servings that comes from grains than from fruits, we would need to know the specific fractions or percentages of each type of food that the student consumes. Without this information, it is impossible to accurately answer the question.

For example, if the student consumes 1/2 of their daily servings from grains and 1/4 of their daily servings from fruits, then the difference would be 1/2 - 1/4 = 1/4 or 25%. However, without knowing the specific fractions or percentages, we cannot determine the difference.

It is important to remember that a balanced diet should include a variety of food groups, including grains, fruits, vegetables, proteins, and dairy. The specific amounts of each will vary depending on individual dietary needs and preferences.

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The rational expression (2x-3)/((2x-3) (2x-3)) satisfies the given constraints.

To create a rational expression with the given constraints, we need to have a binomial in the numerator that cancels out with a binomial in the denominator to produce the desired expression, (1)/(2x-3).

One way to do this is to multiply the desired expression by a binomial that is the same as the one in the denominator. This will give us a rational expression with the desired constraints.

For example, we can multiply (1)/(2x-3) by (2x-3)/(2x-3) to get:

(1 * (2x-3))/((2x-3) * (2x-3))

Simplifying the numerator and denominator gives us:

(2x-3)/((2x-3)(2x-3))

This rational expression has a binomial in the numerator and simplifies to the desired expression, (1)/(2x-3).

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The probability that the selected chocolate will be either cookies and cream or peanut butter cups are,

let cookies and cream be x

and peanut butter cups be y

As these are the two chocolates in the bag,

there is a 50:50 probability

Hence,

The probability of cookies and cream = 50%

The probability of peanut butter cups=50%

As x+y=total both have equal probability

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