7/9 divided by 3/4 WITH A MODEL;)

Answer:

\(a>-1\)

Explanation:

\(5+6a>-1\)

group variables

\(6a>-1-5\)

simplify

\(6a> -6\)

divide both sides by 6

\(a>-1\)

Answer:

a > -1

Step-by-step explanation:

5 + 6a > -1

-5          -5

6a > -6

/6      /6

a > -1

Hope this helps!

Answer:

750 N

Step-by-step explanation:

As the seesaw is balanced, the torque on both ends must be equal.
Weight of the student is 250 N at 2.4 m from the axis
Let the father's weight be x N, at 0.8 m from the axis
= fd
So, 250 * 2.4 = 0.8 * x
Solving for x, the father's weight is 750 N

Answer:

A

Step-by-step explanation:

when you open the brackets you do 5 to the power of 5 and X to the power of 5

As far as we are aware, a straight angle is defined as 180 degrees then the bi-conditional assertion is true.

It combines the conditions "if two line segments are congruent then they are of equal length" and "if two line segments are of equal length then they are congruent." Only when both conditionals are true does a biconditional hold. The symbol "or" is used to denote bi-conditionals.

A statement with two conditions is one that has the form "p if and only if q." In other words, if p, then q and if q, then p. "P iff q" or "p q" are other ways to express the biconditional "p if and only if q."

Since we have given that

1)  If and only if the angle's measurement is 90 degrees, it is a right angle : True.

As is common knowledge, one angle in a right-angled triangle must be 90 degrees.

2) If and only if an angle is obtuse, it measures 120 degrees : True

Obtuse angle is a term used to describe angles that are more than 90° but less than 180°.

And 90°<120°<180°

3) Only if the angle is a straight angle does it measure 180 degrees : True

As far as we are aware, a straight angle is defined as 180 degrees.

As a result, every bi-conditional assertion is true.

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Answer: b⁶

Step-by-step explanation:

The for bⁿ can be optained by multiplying 3 and 2. If there is an exponent on the outside of the parenthesis, you multiply it with the exponent on the inside.

(b³)²=b³ˣ²=b⁶

The percentage strength of neomycin in the final compounded product is approximately 2.5%.

To determine the percentage strength of neomycin in the final compounded product, we need to calculate the weight of neomycin in the cream and divide it by the total weight of the cream.

Neomycin (5%) cream: 30g

The neomycin content is 5% of the total cream weight. To find the weight of neomycin in the cream, we multiply the cream weight by the neomycin percentage:

Weight of neomycin = 30g × 0.05 = 1.5g

Now, to calculate the percentage strength of neomycin in the final compounded product, we divide the weight of neomycin by the total weight of the cream and multiply by 100:

Percentage strength of neomycin = (Weight of neomycin / Total weight of cream) × 100

Percentage strength of neomycin = (1.5g / 60g) × 100 ≈ 2.5

Therefore, the percentage strength of neomycin in the final compounded product is approximately 2.5%.

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The constant rate of change and initial value for the given graph are 40 and 20 respectively. the initial value might represent the fixed cost of the soil.

The slope of a straight line is the tangent of the angle formed by it with the positive x axis as the reference. The negative slope indicates the rate of decrease while the positive shows the rate of increase.

The given problem can be solved as follows,

(a) The graph given is a straight line that passes through (0, 40) and (10, 240).

The constant rate of change is equivalent to the the slope of the line given as,

⇒ (240 - 40)/(10 - 0) = 20

(b) The initial value of the graph is given as the y-intercept of the line.

Which is given as 40.

It might represent the fixed cost.

Hence, the constant rate of change is given as 40 and the initial value is 20 which might represent the fixed cost.

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The missing graph is attached here.

Answer:

so 14 can go into 28, 2 times and 19 can go into 38 2 times so the techaer can make 2 group with 14 girls and 19 boys in each group.

Step-by-step explanation:

the 95% confidence interval for the proportion of all dies that pass the probe is [0.513,0.616].

Sampling is frequently used to estimate the percentage of population that possesses a particular attribute, such as the percentage of all faulty goods which come off an assembly line or the percentage among all buyers that enter a store and make a purchase before leaving. The population proportion is indicated p, while the sample proportion is written p. Thus, if 43% of individuals visiting a business make a purchase before departing, p = 0.43; if 78 people enter the store and make a transaction, p=78/200=0.39.

The sample proportion is a random variable because it differs from sample to sample in ways that are impossible to anticipate in advance. When seen as a random variable, it will be represented by the letter P.

How to solve?

An article reported that in a study of a particular wafer inspection process, 356 dies were examined by an inspection probe and 169 of these passed the probe.

So,p'=201/356=0.56460

The 95% confidence interval for the proportion of all dies that passed the probe will be,

p∈[p'±zα/2√p'(1−p')/n]

p∈[0.56460±1.96×√0.56460(1−0.56460)356]

p∈[0.513,0.616]

So the 95% confidence interval is [0.513,0.616].

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Answer:

x=9

if so

10(2x-3)=1,x

x= 9

Step-by-step explanation:

The equation for the given scenario is 2(3x-6)=18 and the solution is 5.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

We have to create a true statement using the digits 0-9 without repeating.

Now, the equation is 2(3x-6)=18

Here, 3x-6=9

3x=15

x=5

Hence, the equation for the given scenario is 2(3x-6)=18.

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By definition, the degree of a polynomial is same as the degree of the term with the highest /largest degree. The power of leading term represents the degree of polynomial. So, option(C) is right one.

A polynomial is an algebraic expression consisting of indeterminates and coefficient terms with Arithmetic operations ( i.e., addition, subtraction, multiplication) and positive-integer powers of variables. An example of a polynomial of a single variable x, is x² − 4x + 9.

So, the required answer is degree of polynomial.

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Answer: D) Yes, because each x value corresponds to exactly one y value

The table doesn't mention x, but usually x is in the left column. Since we don't have any repeated x values here, this means each input goes to exactly one output. So we have a function.

Visually if you plotted all the points, you'll see the graph passes the vertical line test.

Answer:

be specific

Step-by-step explanation:

which shaded eing

The solution to the system of equations in this problem is given as follows:

The system of equations for this problem is defined as follows:

From the first equation, we have that:

ab^6 = 42

a = 42/(b^6)

a = 42b^(-6).

Replacing on the second equation, we have that the value of b is obtained as follows:

15 = 42b^(-6) x b^9

15 = 42b³

b = (15/42)^(1/3)

b = 0.71.

Then the value of a is obtained as follows:

a = 42 x (0.71)^(-6)

a = 327.9.

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a. As S satisfied the closure under addition, closure under scalar multiplication and non-empty condition S is a subspace of V.

b. The dimension of S is 6.

a. To show that S is a subspace of V, we need to verify that it satisfies the three subspace axioms:

i. Closure under addition:

Let A and B be two matrices in S.

We need to show that A + B is also a lower triangular matrix.

Since A and B are lower triangular, we know that their sum will also be a lower triangular matrix because the sum of two lower triangular matrices is still lower triangular. Therefore, A + B is in S and S is closed under addition.

ii. Closure under scalar multiplication:

Let A be a matrix in S and c be a scalar.

We need to show that c A is also a lower triangular matrix.

Since A is lower triangular, c A will also be lower triangular because multiplying each element in a lower triangular matrix by a scalar will not change its lower triangular form.

Therefore, c A is in S and S is closed under scalar multiplication.

iii. non-empty:

The zero matrix is a lower triangular matrix, so it is in S.

Therefore, S is a subspace of V.

b. To find a basis for S, we need to find a set of linearly independent vectors that span S.

Let's consider the matrix entries in a lower triangular matrix A:

a11    0       0

a21   a22   0

a31   a32   a33

We can see that the entries above the diagonal (a21, a31, and a32) can take any real value, while the entries on the diagonal (a11, a22, and a33) can also take any real value but the entries below the diagonal (all zeros) are fixed.

Therefore, we can construct a basis for S using these fixed entries:

B = {

     [ 1   0  0 ]

     [ 0   1 0  ]

     [ 0  0  1 ]

     [ 0  0  0 ]

     [ 0  0  0 ]

     [ 0  0  0 ]

  }

The dimension of S is equal to the number of elements in its basis, which is 6.

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

Work Shown:

Sum the integers to get 222

(first)+(second)+(third)+(fourth) = 222

(x)+(x+1)+(x+2)+(x+3) = 222

4x+6 = 222

4x = 222-6

4x = 216

x = 216/4

x = 54 is the first integer

x+1 = 54+1 = 55 is the second integer

x+2 = 54+2 = 56 is the third integer

x+3 = 54+3 = 57 is the fourth integer

The sequence is 54, 55, 56, 57

Check:

54+55+56+57 = 222

Answer:

115.395 min

Step-by-step explanation:

First we find the volume of 6 cm of water. We use the formula:

\(\pi *radius^2 *height\)

\(\pi *35^2*6 = 23,079 cm^3\)

1 L/min = 1000 cm^3 / min

0.2 L/min = 200 cm^3 /min

\(\frac{23,079}{200} = 115.395 min\)

The equation that would help the mathematician model the surface area of a square piece of paper as it was repeatedly cut is \(y = 36 \times \frac{1}{2}^x\)

Option D is the correct answer.

We have,

In this equation, the variable x represents the number of times the square is cut in half, and y represents the surface area of the square.

As x increases, the exponent of 1/2 decreases, causing the value of y to decrease.

This exponential decay accurately represents the idea that the surface area becomes less and less but never reaches zero units²

Thus,

The equation that would help the mathematician model the surface area of a square piece of paper as it was repeatedly cut is \(y = 36 \times \frac{1}{2}^x\).

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The correct equation that would help model the surface area of a square piece of paper as it is repeatedly cut in half is:  \(\(y=36(\frac{1}{2})^x\)\)

As the square is cut in half, the side length of the square is divided by 2, resulting in the area being divided by \(\(2^2 = 4\)\).

Therefore, the equation \(y=36(\frac{1}{2})^x\)\)accurately represents the decreasing surface area of the square as it is repeatedly cut in half.

and, \(\(y=x^2+4x-16\)\)is a quadratic equation that does not represent the decreasing nature of the surface area.

and, \(\(y=-25x^2\)\) is a quadratic equation with a negative coefficient.

and, \(\(y=9(2)^x\)\)represents exponential growth rather than the decreasing nature of the surface area when the square is cut in half.

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In ANOVA (Analysis of Variance), the total variability in the data is partitioned into two components: True. The within-treatments variance in an ANOVA provides a measure of the variability inside each treatment condition.

In ANOVA (Analysis of Variance), the total variability in the data is partitioned into two components: the between-treatments variability and the within-treatments variability. The between-treatments variability represents the differences among the treatment conditions, while the within-treatments variability measures the variability within each treatment condition.

The within-treatments variance, also known as the error variance or residual variance, quantifies the variation that cannot be attributed to the differences among treatment conditions. It captures the random variability within each treatment group, accounting for the individual differences and random errors present within the groups.

By analyzing the within-treatments variance, we can assess how much variation exists within each treatment condition and evaluate the consistency or homogeneity of the data within each group. It helps determine the extent to which the treatment conditions explain the observed differences and whether any remaining variation is due to random fluctuations or other factors.

Hence, the statement that the within-treatments variance provides a measure of the variability inside each treatment condition is true in the context of ANOVA.

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Answer:

4

Step-by-step explanation:

Simplifying

5a + -4 = 2a + 8

Reorder the terms:

-4 + 5a = 2a + 8

Reorder the terms:

-4 + 5a = 8 + 2a

Solving

-4 + 5a = 8 + 2a

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-2a' to each side of the equation.

-4 + 5a + -2a = 8 + 2a + -2a

Combine like terms: 5a + -2a = 3a

-4 + 3a = 8 + 2a + -2a

Combine like terms: 2a + -2a = 0

-4 + 3a = 8 + 0

-4 + 3a = 8

Add '4' to each side of the equation.

-4 + 4 + 3a = 8 + 4

Combine like terms: -4 + 4 = 0

0 + 3a = 8 + 4

3a = 8 + 4

Combine like terms: 8 + 4 = 12

3a = 12

Divide each side by '3'.

a = 4

Simplifying

a = 4

Answer:

Area of a triangle=1/2bh

>>1/2×3×6=9

Area of rectangle=L×B

=7*6=42

=7×4=28

Surface Area=2(9)+2(42)+2(28)

=18+84+56=158cm^2

A polynomial can have as many real zeros as its degree, hence one with three degrees can have as many as three zeros.

The roots of an equation are the solution of that equation since an equation consists of hidden values of the variable to determine them by different processes and then the resultant is called roots.

A polynomial with n degrees can have as many variables as n in total.

For example, a quadratic equation ax² + bx + c = 0 is a two-degree equation so it has a maximum of two roots or zeros.

A polynomial with the given degree structure will have exactly 3 roots because it has 3 degrees.

Hence "The maximum number of real zeros in a polynomial will be same as its degree thus 3 degrees will have 3 zeros".

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Subtrahend: 2/32

\(\implies \dfrac{2}{32} \implies \dfrac{1 \times 2}{16 \times 2} \implies \underlin\dfrac{1}{16}\)

The LCM of the denominators in the subtraction problem (5/8 - 2/32) can be determined by writing the multiples of 16 (Simplified denominator) and 8.

Writing the multiples of the denominators (16 and 8):

Since we can see that 16 is a common multiple and is has the least value in both multiples, 16 is the common multiple of 8 and 16.

Multiply such number to the denominators such that the denominators are equivalent to the LCM. Keep in mind that the number we multiply in the denominator must be multiplied to the numerator.

    \(\implies \dfrac{5}{8} - \dfrac{1}{16}\)

    \(\implies \dfrac{5 \times x}{8 \times x} - \dfrac{1}{16} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [8x = \text{LCM}]\)

    \(\implies \dfrac{5 \times 2}{8 \times 2} - \dfrac{1}{16} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [8 \times x = \text{LCM} \implies 8 \times x = 16 \implies x = 2]\)

    \(\implies \dfrac{10}{16} - \dfrac{1}{16}\)

    \(\implies \dfrac{10}{16} - \dfrac{x}{16x} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [16x = \text{LCM}]\)

    \(\implies \dfrac{10}{16} - \dfrac{1 \times 1}{16 \times 1} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [16 \times x = \text{LCM} \implies 16 \times x = 16 \implies x = 1]\)

    \(\implies \dfrac{10}{16} - \dfrac{1}{16}\)

Finally, let's subtract the fractions as the fractions have like denominators.

\(\implies \dfrac{9}{16}\)

Therefore, the simplified fraction is 9/16.

Parts of a subtraction problem:

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none of the provided options (a, b, c, d) appear to be accurate or close to the minimum space required.

To determine the minimum space required for a male restroom design with the given plumbing requirements, we need to consider the minimum space required for water closets and lavatories.

The minimum space required for water closets is typically around 30-36 inches per unit, and for lavatories, it is around 24-30 inches per unit.

Since the design requires a minimum of 12 water closets and 13 lavatories, we can estimate the minimum space required as follows:

Minimum space required for water closets = 12 water closets * 30 inches = 360 inches

Minimum space required for lavatories = 13 lavatories * 24 inches = 312 inches

Adding these two values together, we get a total minimum space requirement of 672 inches.

Among the given options, the closest value to 672 inches is option d) 249. However, this value seems significantly lower than the expected minimum space requirement.

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Answer:

The correct answer is

b) Below 0

The correct option is (d) To the left of 0.

If the graph for a linear regression crosses the y-axis in negative values, the y-intercept of the regression line would be located to the left of 0 on the y-axis.

Therefore, the correct option is (d) To the left of 0. How to find the y-intercept of the regression line?

The y-intercept of a regression line is the value where the regression line intersects with the y-axis. It is the point where x = 0. In order to find the y-intercept of the regression line, we can use the equation of the regression line, which is y = mx + b. Here, m is the slope of the line and b is the y-intercept.

Therefore, if the regression line crosses the y-axis in negative values, it means that the y-intercept (b) is negative, and the line intersects the y-axis to the left of 0.

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Answer:

THere are 33 quarters and 151 nickles

Step-by-step explanation:

Let q be the number of quarters in the bag

Let n be the number of nickles in the bag

Because there are a total of 184 we have a equation:

q + n = 184

Because the total value of the coins is $15.80 so we have another equation

0.25q + 0.05n = $15.80

<=> q + 0.2n = 63.2

We have q + n - (q + 0.2n) = 184 - 63.2

<=> 0.8n = 120.8

<=> n = 151

<=> q = 184 - 151 = 33

The average angular velocity during the dive is option b, 3 π/ √2=rad/s.

The height of the platform, h = 10 m

The number of revolutions made by the diver = 2.5 revolutions = 5π radThe initial velocity of the diver = 0

The final velocity of the diver:

We know,

The formula for final velocity in terms of initial velocity, acceleration, and distance is given as;

v² = u² + 2

Here, Initial velocity, u = 0

Final velocity, v =

Acceleration due to gravity, a = 9.8 m/s²

Distance, s = h = 10 m

Therefore, v² = 0 + 2 × 9.8 × 10v²

   = 196v = √196v = 14.00 m/s

We know, the formula for average angular velocity is given as;

ω = θ/t

Here, angular displacement, θ = 5π rad

Time taken, t

We know, the formula for time taken is given as;

t = √2h/g

Here, height of the platform, h = 10 m

Acceleration due to gravity, g = 9.8 m/s²

Therefore,t = √2 × 10/9.8t = 1.427 s

Substituting the values of θ and t in the formula for average angular velocity, we get;

ω = θ/tω = 5π/1.427ω = 3.5 π/ √2rad/s

Therefore, the average angular velocity during the dive is option b, 3 π/ √2=rad/s.

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