4.
1
Solve for m in the following equation: 7m +
2 = 24.

Solve for m in the following equation 4/7m + 1/4n =24

Answer:

a. [tex]\mathbf{P(\overline x < 68) = 0.9998}[/tex]

b. [tex]\mathbf{P(68 < \overline x < 69 ) =0}[/tex]

c. [tex]\mathbf{P ( \overline x > 66 ) =0.02275}[/tex]

Step-by-step explanation:

Given that ;

Let Y be a random variable In a​ population, where:

mean [tex]\mu_y[/tex] = 65

[tex]\sigma^2_y[/tex] = 49

standard deviation σ  = [tex]\sqrt{49}[/tex] = 7

The objective is to determine the following :

In a random sample of size n​ = 69​, find Pr(Y <68) =

Using the Central limit theorem

[tex]P(\overline x < 68) = \begin {pmatrix} \dfrac{\overline x - \mu }{\dfrac{\sigma}{\sqrt{n}}} < \dfrac{68 - \mu }{\dfrac{\sigma}{\sqrt{n}}} } \end {pmatrix}[/tex]

[tex]P(\overline x < 68) = \begin {pmatrix}Z < \dfrac{68 - 65 }{\dfrac{7}{\sqrt{69}}} } \end {pmatrix}[/tex]

[tex]P(\overline x < 68) = \begin {pmatrix}Z < \dfrac{3 }{\dfrac{7}{8.3066}} } \end {pmatrix}[/tex]

[tex]P(\overline x < 68) = (Z < 3.5599 )[/tex]

From the z tables:

[tex]\mathbf{P(\overline x < 68) = 0.9998}[/tex]

In a random sample of size n​ = 124​, find Pr (68< Y <69)=

[tex]P(68 < \overline x < 69 ) = P \begin {pmatrix} \dfrac{68- \mu}{\dfrac{\sigma}{\sqrt{n}}} < \dfrac{\overline x - \mu}{\dfrac{\sigma}{\sqrt{n}}} < \dfrac{ 69 - \mu}{\dfrac{\sigma}{\sqrt{n}}} \end {pmatrix}[/tex]

[tex]P(68 < \overline x < 69 ) = P \begin {pmatrix} \dfrac{68- 65}{\dfrac{7}{\sqrt{124}}} < Z < \dfrac{ 69 - 65}{\dfrac{7}{\sqrt{124}}} \end {pmatrix}[/tex]

[tex]P(68 < \overline x < 69 ) = P \begin {pmatrix} \dfrac{3}{\dfrac{7}{11.1355}} < Z < \dfrac{ 4}{\dfrac{7}{11.1355}} \end {pmatrix}[/tex]

[tex]P(68 < \overline x < 69 ) = P \begin {pmatrix} 4.7724 < Z < 6.3631 \end {pmatrix}[/tex]

[tex]P(68 < \overline x < 69 ) = P( Z < 6.3631 ) - P ( Z < 4.7724 )[/tex]

From z tables

[tex]P(68 < \overline x < 69 ) = 0.9999 - 0.9999[/tex]

[tex]\mathbf{P(68 < \overline x < 69 ) =0}[/tex]

In a random sample of size n​ = 196​, find Pr (Y >66)=

[tex]P ( \overline x > 66 ) = P ( \dfrac{\overline x -\mu }{\dfrac{\sigma}{\sqrt{n}}} > \dfrac{66 -\mu }{\dfrac{\sigma}{\sqrt{n}}})[/tex]

[tex]P ( \overline x > 66 ) = P ( Z> \dfrac{66 - 65 }{\dfrac{7}{\sqrt{196}}})[/tex]

[tex]P ( \overline x > 66 ) = P ( Z> \dfrac{1 }{\dfrac{7}{14}})[/tex]

[tex]P ( \overline x > 66 ) = P ( Z> \dfrac{14 }{7})[/tex]

[tex]P ( \overline x > 66 ) = P ( Z>2)[/tex]

[tex]P ( \overline x > 66 ) = 1 - P ( Z<2)[/tex]

from z tables

[tex]P ( \overline x > 66 ) = 1 - 0.9773[/tex]

[tex]\mathbf{P ( \overline x > 66 ) =0.02275}[/tex]

Answer:

A.

Step-by-step explanation:

the product of two irrational numbers

Answer:

the answer is A

Step-by-step explanation:

A. the product of two irrational numbers.

Answer: 140°

Step-by-step explanation:

If you look at ∠BXF, you can see that F is at the base of the inner semi circle. Going left, you can see that it stops at 140. Now, we know that m∠BXF is 140°.

Answer:

  m∠BXF = 140°

Step-by-step explanation:

The symbol "<" is "greater than." The symbol "∠" is "angle." When used as "m∠", it refers to "the measure of angle ...".

Here, you're asked for the measure of angle BXF.

You can see that it is an obtuse angle, so will have a measure greater than 90°. The protractor has two scales: one measuring angles counterclockwise, and the other measuring angles clockwise. Ray XF is aligned with the 0 on the inner (counterclockwise) scale, so the angle measure is found where ray XB crosses that scale.

Ray XB crosses the inner scale of the protractor at 140, so ...

  m∠BXF = 140°.

Answer:

x² - 10x - 7

Step-by-step explanation:

See steps below:

Answer:

Answer: There is 1 1/2 times more juice than ginger ale; there is 2/3 as much ginger ale as there is punch.

Step-by-step explanation:

Answer:

Answer A:

Step-by-step explanation:

2 parts ginger ale to 3 parts raspberry juice.

Answer:

See below.

Step-by-step explanation:

So we have the two functions:

[tex]f(x)=-3x\text{ and } g(x)=2x-1[/tex]

And we want to find f(x) + g(x).

So, substitute:

[tex]f(x)+g(x)\\=(-3x)+(2x-1)[/tex]

Combine like terms:

[tex]=(-3x+2x)+(-1)[/tex]

Simplify:

[tex]=-x-1[/tex]

So:

[tex]f(x)+g(x)=-x-1[/tex]

Answer:

The p-value of the test is 0.049.

Step-by-step explanation:

The dependent t-test (also known as the paired t-test or paired samples t-test) compares the two means associated groups to conclude if there is a statistically significant difference amid these two means.

In this case a paired t-test is used to determine whether the experimental toothbrush was effective or not.

The hypothesis for the test can be defined as follows:

H₀: The experimental toothbrush was not effective, i.e. d = 0.

Hₐ: The experimental toothbrush was effective, i.e. d < 0.

The information provided is:

 [tex]\bar d=5.5\\S_{d}=11.6\\n=14[/tex]

Compute the test statistic value as follows:

 [tex]t=\frac{\bar d}{S_{d}/\sqrt{n}}[/tex]

   [tex]=\frac{5.5}{11.6/\sqrt{14}}\\\\=1.7740617\\\\\approx 1.774[/tex]

The test statistic value is 1.774.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.

Compute the p-value of the test as follows:

 [tex]p-value=P(t_{n-1}<1.774)[/tex]

                [tex]=P(t_{13}<1.774)\\=0.049[/tex]

*Use a t-table.

The p-value of the test is 0.049.

p-value= 0.049 > α = 0.05

The null hypothesis will be rejected.

Thus, it can be concluded that experimental toothbrush was effective.

Answer:

The distributive property is used when we have to multiplicate a parenthesis:

[tex]a*(b+c) = ab+ac[/tex]

So the corrects andwer is A) 3x + 4(y-z) = 3x + 4y - 4z, because:

[tex]3x + 4(y-z) = 3x + 4*y + 4*(-z) = 3x + 4y - 4z[/tex]

B is incorrect, as [tex]3x + 3y + 3z 27\neq xyz[/tex]

C is correct, as a number plus his opposite is always 0.

D is correct, but that's the associate property as it's correct that for any three numbers of an associative set, there's another operation with verifies the equality.

Answer:

0=0

Step-by-step explanation:

50x+34=50x+34

50x=50x

50x - 50x = 50x - 50x

0=0

Answer:

5(6x + 2)+4(5x+5)+4=50+34

multiply it then collect like terms

30x+15x+10+15+15+4=50+34

45x +54=50+34

so the 54 will cross over to the other side making it to be -54

45x=50+34-54

45x=30

the u divide both sides by 45

x= 45÷30

x=0.67

Answer:

1456

Step-by-step explanation:

If there are parentheses what is inside comes first, then multiplication or division, last is addition and subtraction. If you have multiple division or multiplication you go in order left to right. Once it's down to addition and subtraction you also go left to right.

First we multiply 284 * 5 = 1420

Now we go in order.

1420 - 6 + 42

1414 + 42

1414 + 42 = 1456

Answer:

Step-by-step explanation:

perimeter = 2(length+width)

then:

15 = 2(a+b)

a = 2b - 4

a = length

b = width

solve:

15/2 = (a+b)

7.5 = ((2b-4) + b) ⇒ Equation that represents the perimeter of the

                             rectangle)

7.5 = 3b -4

7.5+4 = 3b

11.5 = 3b

b = 11.5/3

b = 3.8333

a = 2b - 4

a = 2*3.8333 - 4

a = 3.6667

Check:

15 = 2(3.8333 + 3.6667)

15 = 2*7.5

Answer:

Step-by-step explanation:

(4 + 9x)^3 represents "the cube of the sum of 4 and 9 times x"

and if we divide by "the product of 5 times x and the difference of x and 1," we get

    (4 + 9x)^3

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

       5x(x - 1)

What exactly do you need to know, or to do?

Answer:

23

Step-by-step explanation:

you add 10m(h) plus 8m(w) plus 15m(l)

Answer:

523.1m²

Step-by-step explanation:

Triangle: 1/2bh=1/2(4)(10)=20x2=40 each

Bottom Rectangle: 15x8=120

Side Rectangles: Since the side is a hypotenuse of a right triangle, it’s the square root of 10²+4²=√116=10.77.  10.77x15=161.55

So the total surface area would be 40+40+120+161.55+161.55=523.1m²

Step-by-step explanation:

Hey, there!

Let's simply solve it.

As there is given that L and M are parallel. Use all the condition or properties of parallel lines.

Here use:

Now,

angle 6= 38° { Vertically opposite angle}.

angle 6 + angle 5 = 180° { as sum of coointerior angles are equal to 180°}

38°+angle 5 = 180°

or, angke 5 = 180°-38°

Therefore, angle 5 = 142°

Now, angle 3 = angle 5 { Vertically opposite angle}

Therefore, the measure of angle 3 is 142°.

[tex]hope \: it \: helps...[/tex]

Answer: 142

Step-by-step explanation:

Answer:

SOHCAHTOA.

we have to use SOH(Sin) here because the theta is 65° and the opposite is 13 while the hypotenuse is x.

which is Sin 65°=13/x.

xSin65°=13.

0.906307787x=13.

x=13/0.9063=14.34403619~14.

Answer:

you have four techniques to choose from: plugging in the x value, factoring, rationalizing the numerator, and finding the lowest common denominator.

hope that helps : )

Which equation correctly shows the multiplication of the means and extremes in the proportion 7.2 ∕ 9.6 = 21.6 ∕ 28.8?

a. 7.2 ⋅ 9.6 = 21.6 ⋅ 28.8

b. 9.6 ⋅ 21.6 = 28.8 ⋅ 7.2

c. 7.2 ⋅ 21.6 = 28.8 ⋅ 9.6

d. 7.2 ⋅ 28.8 = 21.6 ⋅ 28.8

Answer:

b. 9.6 ⋅ 21.6 = 28.8 ⋅ 7.2

Step-by-step explanation:

When a proportion say a/b = c/d is given, the outer terms are called the extremes while the inner/middle terms are called the means.

In the case of a / b = c / d,

the outer terms are a and d

the inner terms are b and c

Often times, we find the cross products of the proportion to test whether the two ratios in the proportion are equal. To do that, we find the product of the extremes and equate it to the product of the means.

In the case of a / b = c / d,

the cross products are a x d and b x c

So if a x d = b x c, then a/b = c/d is a true proportion.

Now to the question;

Given proportion: 7.2 / 9.6 = 21.6 / 28.8

Extremes = 7.2 and 28.8

Means = 9.6 and 21.6

The correct multiplication of the means and extremes is therefore

9.6 x 21.6 = 7.2 x 28.8

or

9.6 · 21.6 = 7.2 · 28.8

Answer:

2, 5, & 6

Step-by-step explanation:

2, because it’s the opposite angle.

5, because it’s parallel.

6, because it’s opposite to 5.

2, 5, & 6 all equal 100°.

1, 3, 4, & 7 all equal 80°.

The angles formed that are congruent to angle measure of 100 degrees when transversal t intersects parallel lines m and n are:

Angle measuring 100 degrees is the given angle measure formed at the point of intersection between line m and transversal t.

Thus, angles that are congruent to 100 degrees will be equal in measure to 100 degrees.

The following are angles congruent to 100 degrees.

<2 is congruent to 100 degrees (vertically opposite angles are congruent).

<5 is congruent to 100 degrees (corresponding angles are congruent).

<6 is congruent to 100 degrees (alternate exterior angles are congruent).

Therefore, the angles formed that are congruent to angle measure of 100 degrees when transversal t intersects parallel lines m and n are:

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(-4)³ = (-4)(-4)(-4) = 16(-4) = - 64

(-7)² = (-7)(-7) = 49

(-)×(-) = +

(-)×(+) = -

Answer:

[tex]\int_C F . dr = \pi[/tex]

[tex]C : x = cost , y = sin t, z = sin^2 t - cos^2 t , 0 \leq t \leq 2 \pi[/tex]

Step-by-step explanation:

Given that:

[tex]F(x,y,z) = x^2yi + \dfrac{1}{3}x^3j +xyk[/tex]

Here C is the curve of intersection of the hyperbolic parabolic [tex]z = y^2 - x^2[/tex] and the cylinder [tex]x^2 +y^2 =1[/tex]

Using Stokes' Theorem

[tex]\int_C F . dr =\int \int \limits_s \ curl \ F. \ds[/tex]

From above ;

S = the region under the surface [tex]z = y^2 -x^2[/tex] and above the circle [tex]x^2+y^2 =1[/tex]

Suppose, we consider [tex]f(x,y,z) =z-y^2+x^2[/tex]

therefore, S will be the level curve of f(x,y,z) = 0

Recall that:

[tex]\bigtriangledown f (x,y,z)[/tex] is always normal to the surface S at the point (x,y,z).

∴

This implies that the unit vector [tex]n = \dfrac{\bigtriangledown f}{|| \bigtriangledown ||}[/tex]

So [tex]\bigtriangledown f = <2x, -2y,1 >[/tex]

Also, [tex]|| \bigtriangledown f ||= \sqrt{4x^2+4y^2+1}[/tex]

Similarly ;

[tex]curl \ F = \begin {vmatrix} \begin{array} {ccc}{\dfrac{\partial }{\partial x} }&{\dfrac{\partial }{\partial y} }& {\dfrac{\partial }{\partial z} }\\ \\ x^2y& \dfrac{1}{3}x^3&xy \end {array} \end{vmatrix}[/tex]

[tex]curl \ F = \langle x ,-y,0 \rangle[/tex]

Then:

[tex]\int \int_s curl \ F .ds = \int \int_s curl \ F .nds[/tex]

[tex]\int \int_s curl \ F .ds = \iint_D curl \ F \dfrac{\bigtriangledown f}{ || \bigtriangledown f||} \sqrt{ (\dfrac{\partial z}{\partial x }^2) + \dfrac{\partial z}{\partial x }^2)+1 } \ dA[/tex]

[tex]\int \int_s curl \ F .ds = \iint_D \dfrac{\langle x,-y,0 \rangle * \langle 2x,-2y,1 \rangle }{\sqrt{4x^2 +4y^2 +1 }} \times \sqrt{4x^2 +4y^2 +1 }\ dA[/tex]

[tex]\int \int_s curl \ F .ds = \iint_D (2x^2 + 2y^2) \ dA[/tex]

[tex]\int \int_s curl \ F .ds = 2 \iint_D (x^2 + y^2) \ dA[/tex]

[tex]\int \int_s curl \ F .ds = 2 \int \limits ^{2 \pi} _{0} \int \limits ^1_0r^2.r \ dr \ d\theta[/tex]

converting the integral to polar coordinates

This implies that:

[tex]\int \int_s curl \ F .ds = 2 \int \limits ^{2 \pi} _{0} \int \limits ^1_0r^2.r \ dr \ d\theta[/tex]

⇒ [tex]\int_C F . dr = 2(\theta) ^{2 \pi} _{0} \begin {pmatrix} \dfrac{r^4}{4}^ \end {pmatrix}^1_0[/tex]

[tex]\int_C F . dr = 2(2 \pi) (\dfrac{1}{4})[/tex]

[tex]\int_C F . dr =(4 \pi) (\dfrac{1}{4})[/tex]

[tex]\int_C F . dr = \pi[/tex]

Therefore, the value of [tex]\int_C F . dr = \pi[/tex]

The parametric equations for the curve of intersection of the hyperbolic paraboloid can be expressed as the equations of the plane and cylinder in parametric form . i.e

[tex]z = y^2 - x^2 \ such \ that:\ x=x , y=y , z = y^2 - x^2[/tex]

[tex]x^2 +y^2 =1 \ such \ that \ : x = cos \ t , y= sin \ t, z = z, 0 \leq t \leq 2 \pi[/tex]

Set them equal now,

the Parametric equation of [tex]C : x = cost , y = sin t, z = sin^2 t - cos^2 t , 0 \leq t \leq 2 \pi[/tex]

Answer: F (-8, -3), G (-3, -5) and H (-1, -7)

Step-by-step explanation:

A rotation of 180° around the origin is equivalent to a reflection over the x-axis, and then another reflection over the y-axis.

Then, if we have a point (x, y) and we do a rotation of 180°, the point will transform into (-x, -y)

Then if at the start the vertices of the triangle are:

F (8, 3), G (3, 5), and H (1, 7).

After a rotation of 180°, the vertices will be:

F (-8, -3), G (-3, -5) and H (-1, -7)

The correct option is the last one.

Answer:

E. This polynomial could be factored by using grouping or the perfect squares methods.

Step-by-step explanation:

x^2 + 2x + 1

There is no greatest common factor

This is a perfect square

a^2 + 2ab+ b^2 = ( x+1)^2

We can factor this  by grouping

x^2 + 2x + 1

(x^2 +x) + (x+1)

x( x+1)  + x+1

Factor out x+1

( x+1)  ( x+1)

This is not the difference of squares since there is no subtraction

Answer:

6=6

True for all a

Step-by-step explanation:

[tex]2a+6=2a+5+1\\\mathrm{Subtract\:}2a\mathrm{\:from\:both\:sides}\\\mathrm{Simplify}\\6=5+1\\\mathrm{Simplify\:}5+1:\quad 6\\\\6 = 6[/tex]

Answer:

infinite solutions

Step-by-step explanation:

2a+6=2a+5+1

Combine like terms

2a+6 = 2a+6

Subtract 2a from each side

6 =6

Since this is always true, we have infinite solutions

Answer:

A

Step-by-step explanation:

━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━  

To simplify a number, you have to find the greatest common factor (of the numerator and the denominator) and divide each number by the greatest common factor.

The greatest common factor of 3 and 12 is 3.

Now divide each 3 and 12 by 3.

3 ÷ 3 = 1

12 ÷ 3 = 4

Now the numerator is 1 and the denominator is 4.

3/12 in reduced form is 1/4.

━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━  

Answer:

3/12 in reduced form is 1/4

Step-by-step explanation:

find GCF for 3 and 12 which is 3 . step 2 divide numerator and denominator by GCd which is 3 and rewrite the fraction = (3/3) / (12/3) which equals 1/4. Thus 1/4 is the simplified fraction for 3/12 your welcome

Answer:

B=1 M=6 D=3

Step-by-step explanation:

the equations are 4M+4D+2B=38

                               M+D+B=10

                              2D=M

step two: 4M+4D+2B=38 (multiply 2nd equation by -4)

               -4M-4D-4B=-40

4M AND 4D cancels out and your left with -2B=-2 B=1

then you take the first equation and subsitute the third equation for M

step three:  M+D+1 =10 (SUBSITUTE B WITH 1)

M+D=9

STEP FOUR: take the last equation (M+D=9) and subsitute 2D=M

2D+D=9

3D=9

D=3

subsitute D=3 into 2D=M  so you get 2(3)=M M=6

DOUBLE CHECK USE THE SECOND EQUATION

M+D+B=1-

6+3+1=10

The required number of mice, deers, and birds are 3, 6, and 1 respectively.

In mathematics, it deals with numbers of operations according to the statements.

Here,
Let the number of mice be x and the number of birds is y
Number of Deers  = 2x
There are a total of 10 animals,
mice + deer + bird = 10
x + 2x + y =  10
3x + y = 10
y = 10 - 3x  - - - - - - -(1)

Legs of mouse = 4
Legs of deers = 4
Legs of birds = 2

Total number of legs = 38
4x + 4 * 2x + 2y = 38
4x + 8x + 2y =38
12x + 2y = 38 - - - - - - - (2)
Solving equations 1 and  2
12x + 2(10 -3x ) = 38
12x + 20 - 6x = 38
6x = 18
x = 3
Put x in equation 1
y = 10 - 3 * 3
y = 1

Now,
Mice= x = 3
Deers = 2x = 2 *3 = 6
Bird = y = 1

Thus, the required number of mice, deers, and birds are 3, 6, and 1 respectively.

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#SPJ2

Answer:

10 square units

Step-by-step explanation:

Answer:

x = 9, AR = 25 , AM = 40

Step-by-step explanation:

Since AM = AR + RM and AM also = 7x-23

7x - 23 = (2x + 7) + 15

7x - 23 = 2x + 22

    +23          +23

7x = 2x + 45

-2x   -2x

5x = 45

x = 9

Now plug x = 9 into 2x + 7 to find AR

AR = 2x + 7

     = 2 (9) + 7

     = 18 + 7

AR  = 25

Now to find AM plug x = 9 into 7x - 23

AM = 7x - 23

      = 7 (9) - 23

      = 63 - 23

AM = 40

To double check, we already know that RM = 15, so add AR + RM to find AM

AM = 25 + 15

AM = 40

Answer:

9 = x

AR = 25

AM =  40

Step-by-step explanation:

AR + RM = AM

2x+7 +15 = 7x - 23

Combine like terms

2x+22 = 7x -23

Subtract 2x from each side

2x+22 -2x = 7x-2x -23

22 = 5x - 23

Add 23 to each side

22+23 = 5x-23+23

45 = 5x

Divide each side by 5

45/5 = 5x/5

9 = x

AR = 2x+7 = 2*9 +7 = 18+7 = 25

AM = 7x-23 = 7*9 -23 = 63-23 = 40

Answer:

1 meter wide

Step-by-step explanation:

5+5=10

2/2=1

Answer:

1

Step-by-step explanation: