The ratio of boys to girls in math class is 2:4. If there are 24 students
in total in the class, how many boys and girls are there?

Answer:

  1 ≤ x < 7/4

Step-by-step explanation:

The function f(x) is defined as increasing on the domain (-8, 4), so the ordering of the arguments is not changed by the function. We can solve the inequality as though f(x) = x, which is increasing everywhere.

  f(4x -3) ≥ f(2 -x²)

  4x -3 ≥ 2 -x² . . . . . . using our assumed definition of f(x)

  x² +4x -5 ≥ 0 . . . . . subtract 2-x²

  (x -1)(x +4) ≥ 0 . . . . factored form; zeros at -4, +1

The values of x that make this true are ones that make the factors have the same signs: x ≤ -4 or x ≥ 1.

The domain of f(x) is -8 < x < 4, so we require the arguments of f be restricted to those values

Left side

  -8 < 4x -3 < 4

  -5 < 4x < 7

  -5/4 < x < 7/4

Right side

  -8 < 2 -x² < 4 . . . . . right side is always true

  x² < 10 . . . . . . . . . . . add x² +8

  |x| < √10 . . . . . . . . . . less restrictive than the the left-side restriction

With the given domain restrictions on f(x), the inequality will be true on the interval ...

  1 ≤ x < 7/4

__

Additional comment

The attached graph shows the left-side function argument (dashed blue) and the right-side function argument (dashed green) with the given domain restrictions. The red curve is the difference in function values for the function defined as above. It is only non-negative between 1 and 1.75 as we found above.

This general behavior is applicable for any f(x) that can be described as in the problem statement. For example, f(x) = √(x+8) also gives an increasing curve for the difference f(4x-3)-f(2-x²) on the interval (-5/4, 7/4) with an x-intercept of +1.

<95141404393>

The logically equivalent statement to p → q is:

~q → ~p

The conditional statement:

p → q

Assuming p and q are propositions, the conditional statement may be expressed as:

"If p holds true, then q follows suit. "

'

Whenever p is true, q is true as well. This implies that if q is false, then p must also be false.

We can rephrase this statement cleverly using the negative propositions, which include the opposite or contradictory statements.

~p  and ~q

These mean:

Not p and Not q respectively.

Then the statement:

"If q is not true, then p is not true"

Is written as:

~q → ~p

So this is the logically equivalent statement.

Read more about conditional statements here:

https://brainly.com/question/27839142

#SPJ1

The Complete Question

Given a conditional statement p → q, which statement is logically equivalent?

~p → ~q

~q → ~p

q → p

p → ~q

Answer:

The test statistic value  t =  1.64 < 2.0086 at 0.05 level of significance

Null hypothesis is accepted

The mean portfolio value for all senior citizen shareholders in this region might not be the same as the mean value reported for their counterparts across the nation

Step-by-step explanation:

Step(i):-

Given mean of the population (μ) =  $183,000

Given mean of the sample (x⁻)  = $198,000

Given standard deviation of the sample (S) =  $65,000.

Mean of the sample size 'n' = 51

level of significance  α = 0.05

Step(ii):-

Null hypothesis : H₀ : There is no significance difference between the means

Alternative Hypothesis :H₁: There is  significance difference between the means

Test statistic

             \(t = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }\)

           \(t = \frac{198,000- 183,000 }{\frac{ 65,000}{\sqrt{51} } }\)

          t =  1.64

Step(iii)

Degrees of freedom  ν = n-1 = 51-1 =50

t₀.₀₅ =  2.0086

The calculated value  t =  1.64 < 2.0086 at 0.05 level of significance

Null hypothesis is accepted

Final answer:-

There is no significance difference between the means

The mean portfolio value for all senior citizen shareholders in this region might not be the same as the mean value reported for their counterparts across the nation

Answer:

Step-by-step explanation: h(t)=-16t2+85

Let h(t)=0 to find when the object will hit the ground

0=-16t2+85

Solve for t=?

We need to get t term on its own

Take 85 from both sides

0-85=-16t2+85-85

-85=-16t2

To get t term on its own

Divide both sides by -16

-85/-16=-16t2/-16

5.3=t2

We have to solve for t squared that means we must take the square root of both sides

the square root of 5.3=gives + or - 2.3 seconds we can't have negative time so discard -2.3 seconds

Answer:

Multiply the two numbers

Step-by-step explanation:

1200 \(units^{2}\)

Answer:

1,200 square units

Step-by-step explanation:

Because 30 x 40 equals 1,200.

Answer:

The first number is 272 and the second number is 273

Step-by-step explanation:

Let x = the first number

Let x+1 = the second number

Consecutive just means two numbers in order like 6 and 7  or 152 and 153.

x + (x+1) = 545  I put the parentheses in so that you can see the first number and the second number.  It is not needed, so I will remove

x + x + 1 = 545  Combine the x's)

2x + 1 = 545  Subtract 1 from both sides of the equation

2x = 544  Divide both sides by 2

x = 272 Is the first number, so the second number is 273

Check:

272 + 273 = 545

Answer:

а²-ab+8b+b²-1=a(a-b)+b(8+b)-1

Answer:D y=94x

Step-by-step explanation:

First dive y and x

Then you multiply the next x and the number that you got.

ALSO I GOT IT RIGHT

D. y = 94x. will be the equation that can be used to model the relationship between x and y.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given, a table is attached below.

Since The data in the table is showing the proportionality feature.

the property of having suitable proportions in terms of size, number, degree, harshness, etc. If a defensive action against an unfair attack results in destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.

Thus,

The ratio of distance and time for the cheetah = 470/5 or 940/10 or 1410/15

Since the time is denoted by "x" (in seconds) and distance is denoted by "y".

So,

y/x  = 470/5

y = 94x

therefore, the equation that can be used to model the relationship between x and y will be  D. y = 94x.

Learn more about algebraic Expression here:

https://brainly.com/question/953809

#SPJ6

The solution is, the percent of error, rounded to the nearest percent is 25%.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

given that,

While viewing a herd of cattle on a ranch, Herbert estimated that there were 750 cattle in the herd.

The actual number of cattle in the herd was 600.

now, we have to find the percent of error, rounded to the nearest percent.

so, we get,

Herbert estimated that there were 750 cattle in the herd.

The actual number of cattle in the herd was 600.

so, error = 750 - 600

              = 150

so, we get,

the percent of error = 150 * 100 / 600

                                 = 25%

Hence, The solution is, the percent of error, rounded to the nearest percent is 25%.

To learn more on percentage click:

brainly.com/question/13450942

#SPJ2

Answer:

David is 55 years old

Morgan is 23 years old

__________________________________________________________

Step-by-step explanation:

Let the age of David = x years

Let the age of Morgan = y years

We are Given:

The sum of David and Morgan's age is 78

7 years ago, David's age was 3 times Morgan's age

__________________________________________________________

Making the equations:

from the first statement, the sum of their ages is 78

So, we can write it as:

x + y = 78

from the second statement,7 years ago, David's age was 3 times Morgan's age

David's age 7 years ago = (x - 7)

Morgan's age 7 years ago = (y-7)

So, we can write the equation as:

(x - 7) = 3(y - 7)

which can be simplified to:

x = 3y - 14

__________________________________________________________

Solving the equations:

We have the 2 equations:

from the first equation, we can say that:

x = 78 - y

Using this value in the second equation:

x = 3y - 14

78 - y=  3y - 14                                                             [since x = 78 - y]

78 + 14 = 4y

4y = 92

y = 23

Using this value in the first equation:

x + y = 78

x + 23 = 78                                                                  [since y = 23]

x = 55

__________________________________________________________

The Age of David and Morgan:

Since we assigned x to the age of David:

David is 55 years old

We assigned y to the age of Morgan. So,

Morgan is 23 years old

Answer:

Hope this saved you ^^

Step-by-step explanation:

To determine the number of babies we can expect among the next 12 children to enroll, we need to calculate the proportion of babies based on the current enrollment data.

Out of the total enrollment so far, there are 3 babies and 6 children of other ages, making a total of 9 children.

Proportion of babies = (Number of babies / Total number of children) = 3 / 9 = 1/3

Now, to estimate the number of babies among the next 12 children, we multiply the proportion of babies by the total number of children to be enrolled:

Number of babies expected = Proportion of babies * Total number of children to enroll

Number of babies expected = (1/3) * 12 = 4

Therefore, based on the current enrollment data, we can expect approximately 4 out of the next 12 children to be babies.

The matching expressions are:

\(i) 3a x 4 = C (12a)\\ii) a^2 x a = A (a^3)\\iii) 6 × 1/2 a^2 = D (3a^2)\)

i) 3a x 4 can be represented as C (12a) since multiplying 3a by 4 gives 12a.

ii) a^2 x a can be represented as A (a^3) since multiplying a^2 by a gives a^3.

iii) \(6 \times 1/2 a^2\) can be represented as D (3a^2) since multiplying 6 by 1/2 and then by a^2 gives 3a^2.

To understand the matching expressions, let's break down each one:

i) 3a x 4:

This expression represents multiplying a variable, 'a', by a constant, 4. The result is 12a, which matches with C (12a).

ii) a^2 x a:

This expression represents multiplying the square of a variable, 'a', by 'a' itself. This results in a^3, which matches with A (a^3).

iii) 6 × 1/2 a^2:

This expression involves multiplying a constant, 6, by a fraction, 1/2, and then multiplying it by the square of 'a', a^2. The final result is 3a^2, which matches with D (3a^2).

Therefore, the matching expressions are:

i) 3a x 4 = C (12a)

ii) a^2 x a = A (a^3)

iii) 6 × 1/2 a^2 = D (3a^2)

for such more question on matching expressions

https://brainly.com/question/12270624

#SPJ8

Given statement solution is :- The actual length of the part is 3751/64 inches.

To find the length of the actual part, you can use the scale factor and the length of the part on the drawing. The formula for finding the actual length is:

Actual Length = Length on Drawing × Scale Factor

In this case, the length on the drawing is given as 3 7/8 inches, and the scale factor is given as 15 ¹/8. Let's calculate the actual length:

Length on Drawing = 3 7/8 inches = (3 × 8 + 7) / 8 = 31/8 inches

Scale Factor = 15 ¹/8

Now we can substitute the values into the formula:

Actual Length = (31/8 inches) × (15 ¹/8)

To perform the multiplication, we can convert the mixed fraction into an improper fraction:

15 ¹/8 = (15 × 8 + 1) / 8 = 121/8

Now we can multiply the fractions:

Actual Length = (31/8) × (121/8)

To multiply fractions, we multiply the numerators together and the denominators together:

Actual Length = (31 × 121) / (8 × 8)

Actual Length = 3751 / 64

Therefore, the actual length of the part is 3751/64 inches.

For such more questions on Scale Factor: Find Actual Length

https://brainly.com/question/28684532

#SPJ8

Answer:

a) 3.5

b) 3.33

c) \(6 - 6\left(\begin{array}{ccc}5\\6\end{array}\right)^{10}\)

Step-by-step explanation:

As given,

A fair die is rolled 10 times

a)

Expected value of Sum of the number in 10 rolls = \(\frac{1}{6}(1+2+3+4+5+6) = \frac{21}{6}\)

                                                                                = 3.5

∴ we get

Expected value of Sum of the number in 10 rolls = 3.5

b)

Ley Y : number of multiples of 3

Y be Binomial

Y - B(n = 10, p = \(\frac{2}{6}\) )

Now,

Expected value = E(Y) = np = 10×\(\frac{2}{6}\)  = 3.33

c)

Let m = total number of faces in a die

⇒m = 6

As die is roll 10 times

⇒n = 10

Now,

Let Y = number of different faces appears

Now,

Expected value, E(Y) = m - m\(\left(\begin{array}{ccc}m-1\\m\end{array}\right)^{n}\)

                                  = \(6 - 6\left(\begin{array}{ccc}6-1\\6\end{array}\right)^{10} = 6 - 6\left(\begin{array}{ccc}5\\6\end{array}\right)^{10}\)

In this exercise we have to use probability knowledge to calculate the times the numbers of a roll, in this way we have to:

a) \(3.5\)

b) \(3.33\)

c) \(6-6\left[\begin{array}{cc}5\\6\2\end{array}\right] ^{10}\)

Given that a fair die is rolled 10 times:  

a) Expected value of Sum of the number in 10 rolls  :

\(\frac{1}{6} (1+2+3+4+5+6)= \frac{21}{6} = 3.5\)                                                                            

b) Using the formula of the binomial that is represented by:

\(Y - B(n = 10, p = \frac{2}{6})\)

Expected value:  \(E(Y) = np = (10)(\frac{2}{6} ) = 3.33\)

c) Looking at the 10 times the roll does, we have that it will be. Let m = total number of faces in a die   that represents m  = 6, as die is roll 10 times that represents n = 10. Now,  Expected value:

\(= E(Y) = m - m \left[\begin{array}{cc}m-1\\m\\ \end{array}\right] \\= 6-6\left[\begin{array}{cc}5\\6\2\end{array}\right] ^{10}\)

See more about probability at brainly.com/question/795909

The equation of the parabola with given vertex and focus is (y-11)² = 36(x-7).

A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line.

The general equation of a parabola is: y = a(x-h)² + k or x = a(y-k)² +h, where (h, k) denotes the vertex. The standard equation of a regular parabola is y² = 4ax.

Given that, Vertex (7, 11), focus (16, 11).

Let us find an equation of the parabola for vertex (h, k)=(7, 11) and focus (16, 11).

It can be observed that both focus and vertex lie on y = 11, thus the axis of symmetry is a horizontal line.

a = 16-7 = 9 as y coordinates are the same.

Since the focus lies to the left of vertex, a = 9

Use the equation (y-11)² = 4×9(x-7)

(y-11)² = 36(x-7)

Therefore, the equation of the parabola with given vertex and focus is (y-11)² = 36(x-7).

To learn more about the equation of a parabola visit:

brainly.com/question/11911877.

#SPJ1

The standard equation of the parabolas with vertex (7, 11) and focus (16, 11) are:

(y - 11)² = 36(x - 7)

A parabola is an equation of a curve, such that any point on the curve is equidistant from a fixed point called the focus and a fixed line called the directrix of the parabola.

We have,

(y - k)² = 4p (x - h) open right

(y - k)² = -4p (x - h) open left

Where focus = (h - p, k)  or (h + p, k) and vertex = (h, k)

Now,

Equation of parabola (y - k)² = -4p (x - h) that open left.

(h, k) = (7, 11)

h = 7 and k = 11

(h - p, k) = ( 16, 11)

h - p = 16

7 - p = 16

7 - 16 = p

p = -9

So,

(y - 11)² = 36(x - 7)

Equation of parabola (y - k)² = 4p (x - h) that open right.

(h, k) = (7, 11)

h = 7 and k = 11

(h + p, k) = (16, 11)

h + p = 16

7 + p = 16

p = 16 - 7

p = 9

So,

(y - 11)² = 36 (x - 7)

Thus,

The standard equation of the parabolas is:

(y - 11)² = 36(x - 7)

(y - 11)² = 36 (x - 7)

Learn more about parabola here:

https://brainly.com/question/21685473

#SPJ1

Answer:112

Step-by-step explanation:

I did it and we doing the same test rn haha. What did you get for the grant one?

Answer:

Therefore, 1 + 2cos a can be expressed as the product of 2 and (cos a/2 + 1).

1 + 2cos a = 2(cos a/2 + 1)

Step-by-step explanation:

We can use the trigonometric identity:

cos 2a = 1 - 2 sin^2 a

to rewrite 1 + 2cos a as:

1 + 2cos a = 1 + 2(1 - sin^2 a/2)

= 1 + 2 - 2(sin^2 a/2)

= 3 - 2(sin^2 a/2)

Now, using another trigonometric identity:

sin a = 2 sin(a/2) cos(a/2)

we can rewrite sin^2 a/2 as:

sin^2 a/2 = (1 - cos a)/2

Substituting this into the expression for 1 + 2cos a, we get:

1 + 2cos a = 3 - 2((1 - cos a)/2)

= 3 - (1 - cos a)

= 2 + cos a

Therefore, 1 + 2cos a can be expressed as the product of 2 and (cos a/2 + 1).

1 + 2cos a = 2(cos a/2 + 1)

Answer:

y=2x+16 is the slope intercept form

Step-by-step explanation:

sorry if its wrong tried!!!

Answer:

Part A - No

Part B - 100 %

Step-by-step explanation:

Part A.

This is because, a fair chance requires that each member has the same probability of being picked.

Since there are 4 towns, a fair chance would be 1/4.That is, 1 out of every town.

Part B

The probability of at least 1 representative after 6 number draws is P(at least 1)  = 1 - P(none from Town 1)

P(none from town 1) = 0

P(at least 1)  = 1 - P(none from Town 1)

P(at least 1)  = 1 - 0 = 1

In percentage 1 × 100 % = 100 %

The given statement "horizontal and vertical lines draw out notice because they appear more visually active than diagonal lines." is false.

In geometry, the term line is referred as the path of a moving point through space.

Here we have given the statement "horizontal and vertical lines draw out notice because they appear more visually active than diagonal lines."

And we need to identify whether the given statement is true or not.

While we looking into the given problem, we know that the diagonal line in a composition is considered to be the most dynamic line and suggests movement along that path and they are straight lines that slant in any direction except horizontal or vertical.

Based on this definition, we have identified that the given statement is false.

To know more about line here.

https://brainly.com/question/25727583

#SPJ4

Answer:

x=34

Step-by-step explanation:

put in equation

x+x+22=90 degrees

2x+22=90

2x=68

x=34

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

Explanation:

A+B = 90 ... complementary angles add to 90 degrees

(x+22) + (x) = 90

x+22+x = 90

2x+22 = 90

2x = 90-22 ... subtract 22 from both sides

2x = 68

x = 68/2 ... divide both sides by 2

x = 34

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

Extra info:

if x = 34, then angle A is x+22 = 34+22 = 56 degrees

Then we can see that A+B = 56+34 = 90, which confirms our answer

we can conclude that 2/3 is not equal to 4/5.

To determine if 2/3 is equivalent to 4/5, we can compare the fractions by checking if their ratios are equal. The ratio of 2/3 can be written as 2:3, while the ratio of 4/5 can be written as 4:5.

To check if the ratios are equal, we can cross-multiply and see if the products are equal. Cross-multiplying means multiplying the numerator of the first fraction with the denominator of the second fraction, and the numerator of the second fraction with the denominator of the first fraction.

For 2/3 and 4/5, we have:

2 * 5 = 10

3 * 4 = 12

Since 10 is not equal to 12, we can conclude that 2/3 is not equivalent to 4/5.

for more questions on equivalent

https://brainly.com/question/2972832

#SPJ8

the matrix [cosθ sinθ; -sinθ cosθ] represents the rotation of a vector by an angle θ in the counterclockwise direction.

The matrix you have provided is the 2x2 rotation matrix for rotating a vector in the two-dimensional plane by an angle of θ in the counterclockwise direction.

To understand how this matrix is derived, let's consider a vector v = [x, y] in the two-dimensional plane. We want to rotate this vector by an angle of θ in the counterclockwise direction.

We can represent the vector v as a column matrix [x, y] and then multiply it by a rotation matrix R(θ) to obtain the rotated vector. The rotation matrix R(θ) is defined as follows:

cos(θ) -sin(θ)

sin(θ) cos(θ)

Multiplying the vector v by the rotation matrix R(θ) gives:

[x', y'] = [x, y] * R(θ)

[x', y'] = [x cos(θ) - y sin(θ), x sin(θ) + y cos(θ)]

Thus, the rotated vector v' is given by:

v' = [x', y'] = [x cos(θ) - y sin(θ), x sin(θ) + y cos(θ)]

We can see that the elements of the rotation matrix R(θ) correspond to the cosine and sine of the rotation angle θ. The matrix element in the first row and first column (cosθ) gives the amount of x that is rotated into the x' direction, while the matrix element in the first row and second column (-sinθ) gives the amount of y that is rotated into the x' direction. Similarly, the matrix element in the second row and first column (sinθ) gives the amount of x that is rotated into the y' direction, while the matrix element in the second row and second column (cosθ) gives the amount of y that is rotated into the y' direction.

Thus, the matrix [cosθ sinθ; -sinθ cosθ] represents the rotation of a vector by an angle θ in the counterclockwise direction.

To know more about rotation matrix  click here:

brainly.com/question/30585139

#SPJ4

The value of m ∠ABC=86° ,because of the cyclic quadrilaterals.

Hence, Option (B) is correct.

Since, We know that,

A cyclic quadrilateral is a four-sided polygon whose vertices all lie on a common circle.

The opposite angles of a cyclic quadrilateral have a total of 180°.

Hence, We can formulate;

m ∠ABC +  m ∠ADC  = 180°

m ∠ABC + 94° = 180°

m ∠ABC = 180° - 94°

m ∠ABC = 86°

Similarly, one can find m∠DCB

m∠DAB +  m∠DCB  = 180°

99° + m∠DCB = 180°

m∠DCB = 180° - 99°

m∠DCB = 81°

Hence, m∠ABC = 86°

Learn more about cyclic quadrilaterals here:

brainly.com/question/14352697

#SPJ1

Answer:

6

Step-by-step explanation:

4 × 9 = \(\sqrt 36\) = \(\sqrt{6}\)

The value of y is 6 units obtained by applying pythagoars's theorem in all possible right-angled triangles.

In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.

From the figure, we have three unknowns x, y, and z and we have 3 right-angled triangles so three equations can be formed.

x² = 4² + y²...(i)

z² = 9² + y²...(ii)

(4 + 9)² = x² + z²

13² = x² + z²...(iii)

Now, Subtracting eqn(ii) from eqn(iii) we have.

  169 = x² + z²

(-)  81 = -(y)² + z²

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

88 = x² + y²...(iv).

Now adding eqn(i) and eqn(iv) we have,

2x² = 104.

x² = 52.

Putting this value in eqn(i) we have,

52 = 16 + y².

y² = 36.

y = 6.

learn more about Pythagoras' theorem here :

https://brainly.com/question/21926466

#SPJ2

Answer:

C

Step-by-step explanation:

the slope is -4 and the y-intercept is -1

hope this helps :3

Answer:

c

Step-by-step explanation:

The graph of linear function y – 2x = 3 is attached. The equation transformed 2 units up and 3 units down are y = 2x + 5 and y = 2x respectively.

In order to graph a linear function, determine the value of y substituting different values of x and plot the resulting coordinates on a graph and connect them with a line. The graph is plotted for the linear function: y – 2x = 3. The slope-intercept form of a linear equation is where one side contains just y and is given in general form: y = mx + b where m is the slope and b is the y-intercept. The slope intercept forms the linear equation is y = 2x + 3.

Function transformation takes a function (and its graph) and, by adding and subtraction, moves the graph around the plane without changing its shape. In order to transform the linear function 2 units up, the graph will move up by 2 units. Hence, the slope-intercept form of transformed equation is y = 2x + 3 + 2, hence y = 2x + 5. In order to transform the linear function 3 units down, the graph will move down by 3 units. Hence, the slope-intercept form of transformed equation is y = 2x + 3 - 3, hence y = 2x.

Learn more about Linear function:

https://brainly.com/question/4025726

#SPJ4