angela mad 85% of the 50 free throws she attempted. How many free throws did angela make?

Turning of head is rooting reflex.

Reflex is defined as the action which is performed without thought. In other words, it is an unconscious behaviour or involuntary movement. Newborns have different reflexes such as rooting reflex, moro reflex, stepping reflex, tonic neck reflex and grasp reflex.

Rooting reflex acts on touch. Based on this, babies feed themself. They start sucking when the roof of their mouth is touched. Moro reflex occurs on sudden sound or movement of high intensity. Tonic neck reflex results in fencing position of baby. Grasp reflex is seen when baby closes their fingers and stepping reflex concerns legs.

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\( = > 3x + 15 + 4x + 12 = 180 \\ = > 7x + 27 = 180 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = > \: 7x = 180 - 27 = 153 \: \: \: \: \\ x = \frac{153}{7} = 21 \\ x = 21\)

The hypothesis statement h: μ < 60 is an example of an alternative hypothesis in a one-tail test is true

A hypothesis is a proposed explanation or prediction for an observation or phenomenon that is based on limited evidence or data. It is a tentative statement or idea that can be tested through further observation, experimentation, or data analysis. Hypotheses are often used in scientific research as a starting point to investigate a research question or problem.

The hypothesis statement "μ < 60" is an example of an alternative hypothesis in a one-tailed test.

In a one-tailed test, the alternative hypothesis is directional and states that the population parameter is either greater than or less than the null hypothesis value.

In this case, the alternative hypothesis states that the population mean is less than 60.

The null hypothesis, in contrast, is typically a statement of "no effect" or "no difference" and is often denoted by H0.

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Answer:

It's 180 degrees? I'm not so sure.

Step-by-step explanation:

Step-by-step explanation:

The sum of the series is

\(\tt{ {\bigg[1\dfrac{2}{3} \bigg]}^{2} + {\bigg[2\dfrac{1}{3} \bigg]}^{2} + {3}^{2} + {\bigg[3\dfrac{2}{3} \bigg]}^{2} + - - 10 \: terms}\)

\( \green{\begin{gathered}\large{\sf{{\underline{Formula \: Used - }}}}  \end{gathered}}\)

\(\boxed{\tt{ \displaystyle\sum_{k=1}^{n}1 = n \: }}\)

\(\boxed{\tt{ \displaystyle\sum_{k=1}^{n}k = \frac{n(n + 1)}{2} \: }}\)

\(\boxed{\tt{ \displaystyle\sum_{k=1}^{n} {k}^{2} = \frac{n(n + 1)(2n + 1)}{6} \: }}\)

\(\large\underline{\sf{Solution-}}\)

Given series is

\(\rm :\longmapsto\: {\bigg[1\dfrac{2}{3} \bigg]}^{2} + {\bigg[2\dfrac{1}{3} \bigg]}^{2} + {3}^{2} + {\bigg[3\dfrac{2}{3} \bigg]}^{2} + - - - 10 \: terms\)

can be rewritten as

\(\rm \:  =  \: {\bigg[\dfrac{5}{3} \bigg]}^{2} + {\bigg[\dfrac{7}{3} \bigg]}^{2} + {\bigg[\dfrac{9}{3} \bigg]}^{2} + {\bigg[\dfrac{11}{3} \bigg]}^{2} + - - - 10 \: terms\)

\(\rm \:  =  \: \dfrac{1}{9}[ {5}^{2} + {7}^{2} + {9}^{2} + - - - 10 \: terms \: ]\)

Now, here, 5, 7, 9 forms an AP series with first term 5 and common difference 2.

So, its general term is given by 5 + ( n - 1 )2 = 5 + 2n - 2 = 2n + 3

So, above series can be represented as

\(\rm \:  =  \: \dfrac{1}{9}\displaystyle\sum_{n=1}^{10}(2n + 3) ^{2} \)

\(\rm \:  =  \: \dfrac{1}{9}\displaystyle\sum_{n=1}^{10}\bigg[ {4n}^{2} + 9 + 12n\bigg]\)

\(\rm \:  =  \: \dfrac{1}{9}\bigg[\displaystyle\sum_{n=1}^{10} {4n}^{2} + \displaystyle\sum_{n=1}^{10}9 + 12\displaystyle\sum_{n=1}^{10}n\bigg]\)

\(\rm \:  =  \: \dfrac{1}{9}\bigg[4\displaystyle\sum_{n=1}^{10} {n}^{2} +9 \displaystyle\sum_{n=1}^{10}1 + 12\displaystyle\sum_{n=1}^{10}n\bigg]\)

\(\rm \:  =  \: \dfrac{4}{9}\bigg[\dfrac{10(10 + 1)(20 + 1)}{6} \bigg] + 10 + \dfrac{4}{3}\bigg[\dfrac{10(10 + 1)}{2} \bigg]\)

\(\rm \:  =  \: \dfrac{4}{9}\bigg[\dfrac{10(11)(21)}{6} \bigg] + 10 + \dfrac{4}{3}\bigg[\dfrac{10(11)}{2} \bigg]\)

\(\rm \:  =  \: \dfrac{1540}{9} + 10 + \dfrac{220}{3} \)

\(\rm \:  =  \: \dfrac{1540 + 90 + 660}{9} \)

\(\rm \:  =  \: \dfrac{2290}{9} \)

Hence,

\(\boxed{\tt{ {\bigg[1\dfrac{2}{3} \bigg]}^{2} + {\bigg[2\dfrac{1}{3} \bigg]}^{2} + {3}^{2} + {\bigg[3\dfrac{2}{3} \bigg]}^{2} + - - 10 \: terms = \frac{2290}{9}}}\)

Applying the properties of a rhombus and the Pythagorean Theorem, the length of one side of the rhombus is: 14.9

Recall:

Thus, given:

Find the length of one side using Pythagorean theorem as shown below:

\(HG = \sqrt{(\frac{1}{2}EG)^2 + (\frac{1}{2}FH)^2 } \\\\\)

\(HG = \sqrt{(\frac{1}{2} \times 22)^2 + (\frac{1}{2} \times 20)^2 } \\\\HG = \sqrt{11^2 + 10^2} \\\\\mathbf{HG = 14.9}\)

Therefore, applying the properties of a rhombus and the Pythagorean Theorem, the length of one side of the rhombus is: 14.9

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Answer:

\( \sqrt{1200 {}^{2} - 687 {}^{2} } \\ \)

Step-by-step explanation:

The Pythagoras Theorem says that

\(a {}^{2} + b {}^{2} \)

equals

\(c {}^{2} \)

and here we have C and A or B

Step-by-step explanation:

=| -9/10|+|7/4|

=9/10 +7/4

\( = \frac{9}{10} + \frac{7}{4} \\ = \frac{53}{20} \\ \)

Option B is the answer

the general solution of the differential equation y'' - y = -6t + 4 is y(t) = C₁e^(t) + C₂e^(-t) + 6t - 8, where C₁ and C₂ are arbitrary constants.

To find the general solution, we first solve the associated homogeneous equation y'' - y = 0. This equation has the form ay'' + by' + cy = 0, where a = 1, b = 0, and c = -1. The characteristic equation is obtained by assuming a solution of the form y(t) = e^(αt), where α is an unknown constant. Substituting this into the homogeneous equation gives the characteristic equation: α² - 1 = 0.

Solving this quadratic equation for α yields two distinct roots, α₁ = 1 and α₂ = -1. Thus, the homogeneous solution is y_h(t) = C₁e^(t) + C₂e^(-t), where C₁ and C₂ are arbitrary constants.

To find a particular solution p(t) for the nonhomogeneous equation, we assume a polynomial of degree one, p(t) = At + B. Substituting p(t) into the differential equation gives -2A - At - B = -6t + 4. Equating the coefficients of like terms on both sides, we obtain -A = -6 and -2A - B = 4. Solving this system of equations, we find A = 6 and B = -8.

Therefore, the particular solution is p(t) = 6t - 8. Combining the homogeneous and particular solutions, the general solution of the differential equation y'' - y = -6t + 4 is y(t) = C₁e^(t) + C₂e^(-t) + 6t - 8, where C₁ and C₂ are arbitrary constants.

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Answer: -24x^2+28x

Step-by-step explanation: -4x*6x-(-4x)*7 to -24x^2+28x

The angle of intersection between the plane and the line is approximately 53.13 degrees.

To find the angle of intersection between the line and the plane, we need to determine the direction vector of the line and the normal vector of the plane.

The direction vector of the line is given as ~v(t) = t〈1,2,3〉+ 〈2,−11,9〉. The direction vector is 〈1,2,3〉.

The normal vector of the plane is the coefficient vector of x, y, and z in the equation 3x + 2y − 4z = 0. Therefore, the normal vector is 〈3, 2, -4〉.

To find the angle between the line and the plane, we can use the dot product formula: cos(theta) = (v · n) / (|v| |n|), where v is the direction vector of the line, n is the normal vector of the plane, and theta is the angle of intersection.

Taking the dot product of the direction vector and the normal vector, we have (1)(3) + (2)(2) + (3)(-4) = 3 + 4 - 12 = -5.

The magnitude of the direction vector is |v| = sqrt(1^2 + 2^2 + 3^2) = sqrt(14), and the magnitude of the normal vector is |n| = sqrt(3^2 + 2^2 + (-4)^2) = sqrt(29).

Substituting the values into the formula, cos(theta) = -5 / (sqrt(14) * sqrt(29)) ≈ -0.349.

Taking the inverse cosine of -0.349, we find theta ≈ 53.13 degrees.

The angle of intersection between the line and the plane is approximately 53.13 degrees.

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When Gregory adds these two numbers, the greatest sum Gregory can get will be 975.

From the information, Gregory forms two different numbers with the digits 1, 2, 3, 4, 5, and 6. Both numbers have 3 digits, and each digit is used only once. If he adds these two numbers, what is the greatest sum Gregory can get?

The greatest 3-digit number that can be formed with the digits 1, 2, 3, 4, 5, and 6 is 654 and the smallest is 123. If Gregory forms these two numbers, the sum of these numbers is 654 + 321 = 975, which is the greatest sum he can get.

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Answer:975

Step-by-step explanation:

uyygu

Using the congruence of triangles, the value of x comes to be 15°

A circle is a locus of a point that moves in a plane such that its distance from a fixed point remains constant.

Connect A to D

So, ∠BAC=53°

From the congruence of triangles

∠BAD=∠CAD =53/2 = 26.5°

Also, ∠BAD=∠ABD (since AD=BD=radius)

So, ∠BDA + ∠BAD + ∠ABD=180°

10x-23 + 26.5+26.5 = 180

10x+30=180

10x=150

x=15°

Hence, Using the congruence of triangles, the value of x comes to be 15°

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Answer:

The Answer is 5,000,000

Hope this helps!!

Answer:

Step-by-step explanation:

y  < 19

hope this helps :)

a) The degree of g(x) is 6.

b) The unique roots of the function is x = 0 , x = -2 , x = -5

c) The roots are x = 0, x = -2, and x = 5.

d) The root with multiplicity 1 is x = 0.

e) The root with multiplicity 2 is x = 5.

f) The root with multiplicity 3 is x = -2.

g)  The a-value is positive.

h) The graph of g(x) will have an upward trend in the long run.

i) The end behavior of g(x) as x tends to infinity is an upward trend

Given data ,

Let the function be represented as g(x)

where g( x ) = ( 3/2)x ( x + 2 )³ ( x - 5 )⁵

Now, the degree of the function g(x) is determined by the highest power of x in the expression.

So, degree = x ( x )³ ( x )² = x⁶

And ,the degree is 6.

b)

To find the unique roots of g(x), we set g(x) equal to zero and solve for x:

g(x) = ( 3/2)x ( x + 2 )³ ( x - 5 )⁵ = 0

Setting each factor equal to zero individually, we find the following roots:

x = 0

x + 2 = 0

So, x = -2

x - 5 = 0

So, x = 5

c)The roots of g(x) are the values of x that make g(x) equal to zero. In this case, the roots are x = 0, x = -2, and x = 5.

d) The root with multiplicity 1 is x = 0.

e) The root with multiplicity 2 is x = 5.

f) The root with multiplicity 3 is x = -2.

g) The "a-value" refers to the coefficient of the leading term in the function. In this case, the leading term is ( 3/2)x ( x + 2 )³ ( x - 5 )⁵. The coefficient of the leading term is (3/2). Since (3/2) is positive, the "a-value" is positive.

h) The positive "a-value" in the function indicates that as x tends to infinity, g(x) will also tend to infinity. This means the graph of g(x) will have an upward trend in the long run.

i) As x approaches negative infinity, g(x) will tend to negative infinity (downward trend).

As x approaches positive infinity, g(x) will tend to positive infinity (upward trend).

Therefore, the end behavior of g(x) as x tends to infinity is an upward trend.

Hence , the function is solved.

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Answer:

Angle A is 30

Angle B is 150

Step-by-step explanation:

So we have the supplementary angles A and B. In other words:

\(A+B=180\)

We are also told that Angle B is 30 more than four times Angle A. In an equation, this is:

\(B=30+4A\)

We now have a system of equations. Solve by substitution of B into the first equation:

\(A+B=180\)

\(A+(30+4A)=180\)

Combine like terms:

\(5A+30=180\)

Subtract 30:

\(5A=150\)

Divide by 5:

\(A=30\)

So, Angle A is 30 degrees.

And since the angles are supplementary, this means that Angle B is 180 minus 30 or 150 degrees.

Answer: present statistical information in clear, meaningful terms.

Step-by-step explanation:

When using statistics, the information gathered should be presented in such a way that it is clear and meaningful as this would allow for the data to be tested using various statistical measures.

If data is unclear, the measures used for the test could be negatively impacted such that the results would not represent the most accurate of interpretations.

To solve the equation we first squared both sides of it, that is:

Now we can use the general formula for quadratic equations, then:

Now that we found two option for x, we have to check which of them is really a solution for the original equation (we have to do this since we squared the original equation to get rid of the root), to do this we plug the values we found to see if the eqaution holds.

If x=1:

hence x=1 is a solution for the original equation.

If x=-2:

since this is not true, x=-2 is not a solution for the original equation.

Therefore, the solution for the equation is x=1.

Answer:

Isosceles Triangle... Btw it's worth 5 points

The ratio of the volume of the cylindrical tank to its surface area will be r / 2.

A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.

Let r be the radius and h be the height of the cylinder.

Then the volume of the cylinder will be

V = π r²h cubic units

Then the surface area of the cylinder will be

SA = 2πrh square units

Then the ratio of the volume of the cylindrical tank to its surface area will be

V / SA = π r²h / 2πrh

V / SA = r / 2

The ratio of the volume of the cylindrical tank to its surface area will be r / 2.

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The percent of sales tax to the nearest tenth of a percent is 6.1%

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

The sales amount is 1.95 and the total amount is 31.94.

The tax percentage will be:

= Sales tax / Total amount × 100

= 1.95/31.94 × 100

= 6.1%

The percentage is 6.1%.

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Therefore , the solution of the given problem of function comes out to be fog(-8)= 622.

A function is a relationship between a collection of sources or one product for each input. Simply described, a function is a group of equations linked to a single, distinct output. A declaration, rule, or law that specifies the relationship between two variables is known as a function in mathematics (the dependent variable). When a rules of this kind is employed, there is just one output. by photographer Alex Federspiel. This sentence provides a y=x2 example. Any input for x has only one output for y. Since x is indeed the input value, y is, by definition, a function of x.

Here,

Given :

f(x) = 3x²-3x - 8

g(x) = -x - 7

To find : fog)(-8)= ?

Thus,

We find

=> F(g(x)) => 3g(x)² -3g(x) - 8

=> f(-x-7) =3⋅(-x-7)²-3⋅(-x-7)-8

At x =-8

=> 3(-8-7)² - 3(-8-7)-8

=> 3(225)-3(15) -8

=> 675 - 45 -8

=> 622

Therefore , the solution of the given problem of function comes out to be fog(-8)= 622.

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The first step in developing a competency-model is to gather background information and analyze the existing standards within the workplace.

The first-step involves conducting a thorough examination of the organization's goals, strategies, and the specific job roles or positions for which the competency-model will be developed.

By gathering background information, organizations can understand the context in which the competency-model will be applied.

Analyzing existing standards within the workplace involves assessing the current performance expectations, competencies, and criteria used for evaluating employees in their respective roles.

The purpose of this step is to identify any gaps or areas for improvement in the existing standards and to ensure that the development of the competency model aligns with the organization's overall objectives.

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The first step in developing a competency model is conducting a job analysis.

developing a competency model is a systematic process that helps organizations define the key competencies needed for their employees. The first step in this process is conducting a job analysis.

A job analysis involves gathering information about the job, such as its purpose, tasks, responsibilities, and required qualifications. This information can be collected through methods like interviews, observations, and surveys. By analyzing the job, organizations can identify the critical competencies that are necessary for effective job performance.

These competencies can then be used to guide various HR processes, including recruitment, selection, training, and performance management. By aligning the competencies with job requirements, organizations can ensure that they have the right people with the right skills in the right positions.

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Isaac pay for the cost of racket is 39.9.

The cost of a pair of shoes is three times the cost of a bag, so we can write:

Cost of shoes = 3b

Similarly, the cost of the racket is twice the cost of the bag, so we can write:

Cost of racket = 2b

Now we can use the given information to set up an equation:

Cost of racket + Cost of bag + Cost of shoes = $119.70

Substituting the expressions we found above, we get:

2b + b + 3b = $119.70

Simplifying the equation:

6b = $119.70

Dividing both sides by 6:

b = $19.95

So the cost of the bag is $19.95.

We can use this to find the costs of the shoes and racket:

Cost of shoes = 3b = 3($19.95) = $59.85

Cost of racket = 2b = 2($19.95) = $39.90

Therefore, Isaac paid $39.90 for the racket.

A cost is an expenditure required to produce or sell a product or get an asset ready for normal use. In other words, it's the amount paid to manufacture a product, purchase inventory, sell merchandise, or get equipment ready to use in a business process.

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Answer:

x = 5

Step-by-step explanation:

Here, from what we have, the angle and the sides facing it are equal

Since we have pi oh both sides

Thus;

6x + 6 = 9x-9

9x-6x = 9 + 6

3x = 15

x = 15/3

x = 5

Answer:

The equation of the line with slope = 3 and point (5, 14)

will be:

Step-by-step explanation:

Given

slope = m = 3

point = (5, 14)

As the point-slope form of the equation of the line is

\(y-y_1=m\left(x-x_1\right)\)

where m is the slope.

substituting the values m = 3 and the point (5, 14)

\(y-14=3\left(x-5\right)\)

Add 14 to both sides

\(y-14+14=3\left(x-5\right)+14\)

\(y=3x-1\)

Therefore, the equation of the line with slope = 3 and point (5, 14)

will be:

\(y=3x-1\)

Answer:

B) 6

Step-by-step explanation:

In a Scatter Plot you must plot all points given therefore you plot B) 6 points