4.
3.
If the base of the triangle is 4.1 cm. and the
height is 5.7 cm., what is the approximate area
bh
of the triangle? (Area of a triangle = home :)
a. 23.3 cm b. 15.5 cm
c. 11.7 cm

Answer:

Entrance fee for children: $1.92

Entrance fee for adults: $3.92

Step-by-step explanation:

Total expenses for this year: $214.00

The child fee will be: $x

and the adult fee will be $(x+2)

Last year the number of children was 44

and the number of adults was 33

this year also has the same number of children and adults.

which means the entrance fee total for children will be $44x and for adults will be $33(x+2).

44x + 33(x+2) = 214

--> 44x + 33x + 66 = 214

--> 77x = 214 - 66 = 148

--> x = 148/77 = 1.92

So children's price is $1.92 and adults price is $1.92 + 2

hence:

Entrance fee for children: $1.92

Entrance fee for adults: $3.92

The two pairs of integers that satisfy the given conditions are (-3, 8) and (5, 24).

To solve the system of equations, let's assign variables to the two integers. Let the first integer be represented by 'x' and the second integer by 'y'.

According to the given information:

a. Fourteen more than twice the first integer gives the second integer:

This can be expressed as: 2x + 14 = y

b. The second integer increased by one is the square of the first integer:

This can be expressed as: y + 1 = x^2

Now, we have a system of equations:

1) 2x + 14 = y

2) y + 1 = x^2

To solve this system, we can substitute the value of 'y' from equation 1) into equation 2):

2x + 14 + 1 = x^2

2x + 15 = x^2

Rearranging the equation, we have:

\(x^2 - 2x - 15 = 0\)

Factoring the quadratic equation, we get:

(x - 5)(x + 3) = 0

Setting each factor equal to zero:

x - 5 = 0   -->   x = 5

x + 3 = 0   -->   x = -3

Substituting the values of 'x' back into equation 1), we can find the corresponding values of 'y':

For x = 5:

2(5) + 14 = y

10 + 14 = y

y = 24

For x = -3:

2(-3) + 14 = y

-6 + 14 = y

y = 8

Therefore, the two pairs of integers that satisfy the given conditions are (-3, 8) and (5, 24).

for more such question on integers visit

https://brainly.com/question/929808

#SPJ8

Answer:

\(2abCosC = 1\)

Step-by-step explanation:

The cosine rule is

=> \(a^2= b^2+c^2-2abCosC\)

For 2abCosC, it becomes

=> \(2abCosC = b^2+c^2-a^2\)

=> \(2abCosC = (2)^2+(1)^2-(2)^2\)

=> \(2abCosC = 1\)

Answer:

25c

Step-by-step explanation:

For example , if there are 3 tanks (or n is 3), the total number of fish would be 25* 3 = 75 fish.

a) The expected May rainfall is 5.0 inches.

b) The probability of May rainfall falling within one standard deviation of the mean is 0.6827, and within two standard deviations is 0.9545.

(a) To calculate the expected May rainfall, we need to find the mean (μx) of the uniform distribution. The mean of a uniform distribution can be found using the formula:

μx = (a + b) / 2

where a and b are the lower and upper limits of the distribution, respectively. In this case, a = 2 and b = 8. So,
μx = (2 + 8) / 2
μx = 10 / 2
μx = 5

(b) To find the probability that the observed May rainfall will fall within one and two standard deviations of the mean, we first need to calculate the standard deviation (σx) of the uniform distribution. The formula for the standard deviation of a uniform distribution is:

\(σx = √((b - a)^2 / 12)\)

Using the values of a and b from before, we have:

\(σx = √((8 - 2)^2 / 12)\)
σx = √(36 / 12)
σx = √3

For a uniform distribution, the probabilities of falling within one and two standard deviations of the mean are as follows:

- Within one standard deviation (±1σx): 68.27% or 0.6827
- Within two standard deviations (±2σx): 95.45% or 0.9545

for such more question on standard deviation

https://brainly.com/question/475676

#SPJ11

Sarah spends reading 30 min + \(0.05 min^{2}\).

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. To assist identify the sequence of operations and other features of logical syntax, mathematical symbols can denote numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.

However, in modern mathematics, and particularly in computer algebra, formulae are considered expressions that may be evaluated as true or false based on the values assigned to the variables in the expressions.

The problem is in a mathematical expression.

30 min+3s min did Sarah spend reading

Convert s to min

.30min+3s min× 1min/60s

Cancel the common units and simplify.

Cross-cancel units.

30 min + \(0.05 min^{2}\)

To learn more about mathematical expression, click

https://brainly.com/question/1703934

#SPJ1

Answer:

a) the mean percentage of defective item produced is 2.52 %

b) the standard deviation of percentage of defective item produced is 1.01%

Step-by-step explanation:

Given that;

the percentage of defective items produced was 2%, 1.4%, 4%, 3%, 2.2%.

sample size n = 5

a) Calculate the mean for these data

mean percentage of defective item produced will be;

\(x^{bar}\) = ∑x / n

\(x^{bar}\) = ∑x / n = ( 2% + 1.4% + 4% + 3% + 2.2% ) / 5

\(x^{bar}\)  = 12.6 / 5

\(x^{bar}\)  = 2.52 %

Therefore, the mean percentage of defective item produced is 2.52 %

b) Calculate the standard deviation for these data

Formula for standard deviation is;

S = √( (∑(x-\(x^{bar}\) )²) / (n-1) )

so we make a table;

x                   ( x - \(x^{bar}\) )%                ( x - \(x^{bar}\) )²%

2%                 -0.52                         0.2704

1.4%               -1.12                           1.2544

4%                  1.48                          2.1904  

3%                  0.48                         0.2304

2.2%.             -0.32                         0.1024

summation                                     4.048

so (∑(x-\(x^{bar}\) )² = 4.048%  

so we substitute the value into our equation;

S = √( (∑(x-\(x^{bar}\) )²) / (n-1) )

S = √( (4.048%) / (5-1) )

S = √( 4.048% / 4 )

S = √( 1.0121

S =  1.00598 % ≈ 1.01%

Therefore, the standard deviation of percentage of defective item produced is 1.01%

\(w^2 - 6w + 4\) is a polynomial that represents how much more profit is earned by selling w apple trees than w pear trees.

The profit earned by selling w pear trees is 2w + 10

To find the difference in profit, we need to subtract the profit earned by selling w pear trees from the profit earned by selling w apple trees:

\((w^2 - 4w + 14) - (2w + 10)\)

Simplifying the expression:

\(w^2 - 6w + 4\)

Therefore, the polynomial that represents how much more profit is earned by selling w apple trees than w pear trees is \(w^2 - 6w + 4\).

Learn more about expression here:

https://brainly.com/question/14083225

#SPJ1

Answer: A

because slope are

The given table does not represent a function. The correct answer is D. No, because one x-value corresponds to two different y-values.

To determine if the table represents a function, we need to check if every x-value corresponds to exactly one y-value. Let's analyze the given table:

x | y

-------

O | 1

X | 4

2 | 3

3 | 2

3 | 5

4 |

5 |

From the table, we can see that the x-values are not unique. Both the values 3 and 4 appear twice in the x-column, but they have different corresponding y-values.

This violates the definition of a function, which states that each input (x-value) should have only one output (y-value).

Therefore, the given table does not represent a function.

The correct answer is D. No, because one x-value corresponds to two different y-values.

for such more question on function

https://brainly.com/question/13473114

#SPJ8

Answer:

P(A or B) = P(A) + P(B) - P(A and B)

0.87 = 0.8 + P(B) - 0.23

0.87 = P(B) + 0.57

P(B) + 0.57 = 0.87

P(B) + 0.57-0.57 = 0.87-0.57

P(B) = 0.3

Answer: 0.3

The value of P(B)= 0.3

It is a branch of mathematics that deals with the occurrence of a random event.

Given:

P(A)=0.8, P(A OR B)=0.87, P(A AND B)=0.23,

Now, using

P(A or B) = P(A) + P(B) - P(A and B)

0.87 = 0.8 + P(B) - 0.23

0.87 = P(B) + 0.57

P(B) + 0.57 = 0.87

P(B) = 0.87-0.57

P(B) = 0.3

Learn more about probability here:

https://brainly.com/question/743546

#SPJ2

Ignore the negative sign, since that only affects the sign of the final product

3415₇ × 432₇

You can compute the product by considering the digit expansion, by which I mean first expanding each number as sums of powers of 7:

3415₇ = 3000₇ + 400₇ + 10₇ + 5₇

(It's the same thing as writing, for example, the decimal 3415 as 3000 + 400 + 10 + 5, just in a different base.)

Similarly,

432₇ = 400₇ + 30₇ + 2₇

Then apply the distributive property:

= (3000₇ + 400₇ + 10₇ + 5₇) × (400₇ + 30₇ + 2₇)

= 3000₇ × (400₇ + 30₇ + 2₇)

… + 400₇ × (400₇ + 30₇ + 2₇)

… + 10₇ × (400₇ + 30₇ + 2₇)

… + 5₇ × (400₇ + 30₇ + 2₇)

= {12}00000₇ + {9}0000₇ + 6000₇

… + {16}0000₇ + {12}000₇ + {8}00₇

… + 4000₇ + 300₇ + 20₇

… + {20}00₇ + {15}0₇ + {10}₇

where I use the curly braces to indicate products (written in base 10) of digits that exceed 6. Anything in these braces needs to be properly converted to base 7. For example,

{12}₇ = 7 + 5 = 15₇

So you would have

= 1500000₇ + 120000₇ + 6000₇

… + 220000₇ + 15000₇ + 1100₇

… + 4000₇ + 300₇ + 20₇

… + 2600₇ + 210₇ + 13₇

Add everything up:

• In the 7⁰ place,

3₇

• In the 7¹ place,

1₇ + 1₇ + 2₇ = 4₇

• In the 7² place,

2₇ + 6₇ + 3₇ + 1₇ = {12}₇ = 15₇

• Carry the 1 (underlined). In the 7³ place,

2₇ + 4₇ + 1₇ + 5₇ + 6₇ + 1₇ = {19}₇ = 25₇

• Carry the 2. In the 7⁴ place,

1₇ + 2₇ + 2₇ + 2₇ = {7}₇ = 10₇

• Carry the 1. In the 7⁵ place,

2₇ + 1₇ + 5₇ + 1₇ = {9}₇ = 12₇

• Carry the 1. In the 7⁶ place,

1₇ + 1₇ = 2₇

So, we end up with

3415₇ × 432₇ = 22045543₇

and thus

3415₇ × (-432₇) = -22045543₇

1. The translation was of 4 units right and 3 units down.

2. All the blue lines connecting the equivalent vertices will have a slope of -3/4.

The translations of the triangle is given by the rule presented as follows:

(x,y) -> (x + 4, y - 3).

Hence the meaning of each of these translations is given as follows:

The coordinates of the original vertices are given as follows:

(0,0), (0,4), (3,0).

Then the coordinates of the translated vertices are given as follows:

(4,-3), (4,1), (7,-3).

For a linear function, the slope is given by the vertical change divided by the horizontal change.

From these translations, the changes are given as follows:

Thus the slope of the linear function connecting the original vertices are given as follows:

m = -3/4.

More can be learned about translations at brainly.com/question/29211183

#SPJ1

The amplitudes of functions are a) 8 and b) 6.

Given are the functions we need to determine the amplitude of function,

a) y = 8 Sin (x/2) + 3

b) y = 6 Cos x + 2

So,

To determine the amplitude of a trigonometric function, you can follow these steps:

For a sine function of the form y = A×sin(Bx + C) + D:

The amplitude is equal to the absolute value of the coefficient A.

For a cosine function of the form y = A×cos(Bx + C) + D:

The amplitude is equal to the absolute value of the coefficient A.

Let's apply these steps to the given functions:

a) y = 8×sin(x/2) + 3

The coefficient of sin in this function is 8, so the amplitude is |8| = 8.

Therefore, the amplitude of function a) is 8.

b) y = 6×cos(x) + 2

The coefficient of cos in this function is 6, so the amplitude is |6| = 6.

Therefore, the amplitude of function b) is 6.

Hence the amplitudes of functions are a) 8 and b) 6.

Learn more about amplitude click;

https://brainly.com/question/9525052

#SPJ1

There is no real Value of k that will satisfy the equation 2x² - x + 8k = 0 if a and 1/a are the roots of the polynomial.

(i) Zeroes of the polynomial:

In the graph, we have two points where the curve intersects the x-axis: one is at (-1,0), and the other is at (2,0).The corresponding values of x are -1 and 2, and they are the zeros of the polynomial. Therefore, the zeros of the polynomial are -1 and 2.(ii) Forming the quadratic polynomial:

From the graph, we can observe that the curve intersects the y-axis at the point (0,5), implying that the constant term of the polynomial is 5.

We can use the formula to find the quadratic polynomial if we have two zeros and one constant term. Thus, the quadratic polynomial is given by:(x + 1)(x - 2) = x² - x - 2x + 2 = x² - 3x + 2. Therefore, the quadratic polynomial is x² - 3x + 2.(iii) Value of k if a, 1/a are the zeroes of the polynomial 2x² - x + 8k:

We know that a and 1/a are the zeroes of the polynomial 2x² - x + 8k. Therefore, we can find the sum and product of the roots and use them to determine the value of k.

The sum of the roots is a + 1/a, and their product is a(1/a) = 1. Using the sum and product of the roots, we can write: a + 1/a = 1/2 (1/2 is the coefficient of x)Substituting a with 1/a in the above equation, we get: 1/a + a = 1/2Multiplying both sides of the equation by 2a, we get: 2 + 2a² = a

Simplifying the equation, we get: 2a² - a + 2 = 0Multiplying both sides by 2,

we get: 4a² - 2a + 4 = 0Dividing both sides by 2, we get: 2a² - a + 2 = 0

Using the quadratic formula, we get: a = [1 ± √(1 - 4(2)(2))]/(2(2))

Simplifying, we get: a = [1 ± √(-31)]/4Since the discriminant of the quadratic formula is negative, the roots are imaginary. Therefore, there is no real value of k that will satisfy the equation 2x² - x + 8k = 0 if a and 1/a are the roots of the polynomial.

For more questions on Value .

https://brainly.com/question/843074

#SPJ8

The given diagram shows a circle with radius (R) 6 inches, and the central angle of arc AB as 30 degrees,

Consider that the length (L) of a circular arc of radius R and central angle Θ, is given by the formula,

$108.50

1 bottle collected= $1.50 + $2.00 + $2.50 = $6.00

2 bottles " = $5.00

3 bottles " = $5.50 + $6.00 = $11.50

4 bottles " = $7.00 + $8.00 = $15.00

5 bottles " = $6.00 + $9.00 + $10.00 = $25.00

6 bottles " = $2.00 + $8.00 + $11.00 + $13.00 = $34.00

7 bottles " = $12.00

Then you add up all the answers to get the final amount Eric earned.

$6.00 + $5.00 + $11.50 + $15.00 + $25.00 + $34.00 + $12.00 = $108.50.

Answer:

C. 139°

Step-by-step explanation:

Given:

m<A = 62°

m<B = 77°

Required:

Find m<1

Solution:

Since ∆ABC is similar to ∆DEF, therefore:

<A ≅ <D, which means m<D = 62°

<B ≅ <E, which means m<E = 77°

<C ≅ <F

Therefore, based on exterior angle theorem:

m<1 = m<D + m<E

m<1 = 62° + 77° (substitution)

m<1 = 139°

The interval of the domain of the considered function for which the function is decreasing is none. The function is strictly increasing: Option D: The function is increasing only.

Suppose that the function is y = f(x)

If for an interval I, when x increases meanwhile staying in the interval I, the function's output decreases (or can stay same), then we say that the function is decreasing in the interval I.

This interval I was of values that x can take for this function, which is the domain of the considered function, so we say:

y = f(x) is decreasing function in an interval I if:

\(f(x+\delta) \leq f(x) \: \forall x \in I : x+\delta \in I\)

If we have:

\(f(x+\delta) < f(x) \: \forall x \in I : x+\delta \in I\), then the function is called strictly decreasing in the interval I.

Similarly, there increasing( \(f(x+\delta) \geq f(x) \: \forall x \in I : x+\delta \in I\) ) and strictly increasing(\(f(x+\delta) > f(x) \: \forall x \in I : x+\delta \in I\) ) functions.

For this case, the function is:

\(h(x) = \left \{ {{2^x, x < 1} \atop \: \atop {\sqrt{x+3}, x \geq 1}} \right.\)

The function is differentiable in either side of 1.

Sign of rate of function at a point tells whether its increasing or decreasing.

\(h'(x)= 2^x ln(2)\)
We know that:

\(2^x > 0 \: \rm \forlall x \in \mathbb R\)

And \(ln(2) \approx 0.69 > 0\)

Thus, \(h'(x)= 2^x ln(2) > 0 \: \forall x \in \mathbb R\)

So, rate is positive, the function is strictly increasing for this case.

\(h'(x) = \dfrac{1}{2\sqrt{(x+3)}}\)

For all x > 1, \(\sqrt{x+3} > 0\), and so as h'(x)

So rate is positive and therefore strictly increasing for this case too.

\(h(1+\delta) - h(1)= \sqrt{1+\delta + 3} - \sqrt{1+3} = \sqrt{4+\delta} - \sqrt{4} > 0 \forall \delta > 0\)

So rate of the considered function is positive,so function is strictly increasing all over the domain.

Thus, the interval of the domain of the considered function for which the function is decreasing is none. The function is strictly increasing: Option D: The function is increasing only.

Learn more about increasing functions here:
https://brainly.com/question/14330051

#SPJ2

Answer:

a)73

b)27

c)58

d)70

Answer:

29.4°

Step-by-step explanation:

The equation can be rearranged to give C directly.

 C = arccos((a^2 +b^2 -c^2)/(2ab))

 C = arccos((90^2 +55^2 -50^2)/(2·90·55))

 C = arccos(8625/9900) ≈ 29.4002°

 C ≈ 29.4°

The measure of angle C is approximately 29.46 degrees.

To find the measure of angle C (cos(C)) using the given values a = 55, b = 90, and c = 50, we can use the Cosine Rule formula:

cos(C) = (a² + b² - c²) / (2 * a * b)

Substitute the given values:

cos(C) = (55² + 90² - 50²) / (2 * 55 * 90)

Now, calculate the numerator:

cos(C) = (3025 + 8100 - 2500) / (2 * 55 * 90)

cos(C) = 8625 / 9900

Now, divide to get the final value of cos(C):

cos(C) ≈ 0.8707

To find the measure of angle C itself, we can take the inverse cosine (arccos) of this value:

C ≈ arccos(0.8707)

Using a calculator, you'll find:

C ≈ 29.46 degrees (rounded to two decimal places)

So, the measure of angle C is approximately 29.46 degrees.

Learn more about  Cosine Rule formula at

https://brainly.com/question/31506605

#SPJ2

Answer:

What is X?

Step-by-step explanation:

4 multiplied by X + 8 =Ps

Answer:

0000–1199

Step-by-step explanation:

Edge 2020/2021

The study described is a randomized experiment.

A randomized experiment is a typical experimental study design. It is a study design in which the researcher or investigator is in complete control of the research environment. For example, an investigator may wish to assess the effects of certain treatments on some experimental units.

The investigator decides the type of treatment, the type of experimental unit to use, and the allocation and assessment procedures of the treatments and effects, respectively, while in an observational study, the researcher or investigator is usually a passive observer as he only observes and analyses facts and events as they occur naturally.

In experimental studies, the researcher is in complete control of the exposure, and the result should therefore provide stronger evidence of an association or lack of association between exposure and a health problem than would an observational study.  

To know more about randomized experiment, here

https://brainly.com/question/10050306

#SPJ4

"Determine whether the study described below is a randomized experiment or an observational study.

A medical researcher wants to determine whether exercise can lower blood pressure. She recruits 100 people with high blood pressure to participate in the study. She assigns a random sample of 50 of them to pursue an exercise program that includes daily swimming and jogging. She assigns the other 50 to refrain from vigorous activity. She measures the blood pressure of each of the 100 individuals both before and after the study."--

Answer:

d 16 minutes

Step-by-step explanation:

1 mile equals 8 minutes

2 miles equals 16 minutes