100 Points! Algebra question. Photo attached. Find the exact value of the expression. Please show as much work as possible. Thank you!

Answer:

[tex]a_{n}=a_{1} r^{n-1}[/tex]

[tex]a_{n}=5 (2)^{n-1}[/tex]

The results of increasing a gross by 10% is 158.4.

Percentage refers to the amount, number or rate of something, regarded as part of a total of 100.

In mathematics, gross is written in figures as 144

increase a gross by 10%

= 144 + (10% × 144)

= 144 + (0.1 × 144)

= 144 + 14.4

= 158.4

Hence, 158.4 is the 10% increase in gross.

Complete question:

Calculate the increase in a gross by 10%.

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The area of the larger square is 900% of the area of the smaller square.

Let's assume that the side of the smaller square is "s". Therefore, the area of the smaller square will be:

Area of smaller square = s²

Now, the sides of the square are increased by a scale factor of 3, which means that the new side length of the larger square will be 3s. The area of the larger square will be:

Area of larger square = (3s)² = 9s²

To find the percentage of the larger square with respect to the smaller square, we need to divide the area of the larger square by the area of the smaller square, and then multiply by 100:

(9s²/s²) x 100 = 900%

This means that the larger square is 9 times the area of the smaller square.

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Answer: 9 fish

Step-by-step explanation:

To find the answer all you have to do is multiply the amount of fish per gallon (0.12) to the total amount to gallons (75).

75 x 0.12 = 9

A 75-gallon aquarium will hold about 8 fish.

Stocking guidelines are 1 inch of adult fish per gallon of tank water. When applying this rule of thumb, we have to keep in mind that a 75 gallons water tank only holds about 70 gallons of water.

Then the number of fish in the tank would be:

Number of fish = density of fish * volume of water in the tank

Number of fish = 0.12 * 70

Number of fish = 8.4

So there are about 8 fish in the tank.

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One-way ANOVA utilizes the five steps of hypothesis testing to determine if there are significant differences among the means of three or more groups.

One-way ANOVA, or analysis of variance, is a statistical test used to compare the means of three or more groups to determine if there are significant differences among them. It helps in determining whether the variations between the group means are due to random chance or if they are statistically significant.

The five steps of hypothesis testing are commonly used in one-way ANOVA to analyze and draw conclusions from the data. These steps are as follows:

1. Formulating the null and alternative hypotheses: In one-way ANOVA, the null hypothesis (H0) states that there are no significant differences between the group means, while the alternative hypothesis (Ha) states that at least one group mean differs significantly from the others.

2. Choosing a significance level: The significance level, denoted as α, represents the threshold below which the null hypothesis is rejected. Commonly used values for α are 0.05 or 0.01, indicating a 5% or 1% chance, respectively, of rejecting the null hypothesis incorrectly.

3. Computing the test statistic: In one-way ANOVA, the test statistic is the F-statistic, which compares the between-group variation to the within-group variation. It measures the ratio of the mean square between (MSB) to the mean square within (MSW).

4. Determining the critical value: The critical value is derived from the F-distribution table and depends on the significance level and the degrees of freedom associated with the numerator and denominator of the F-statistic.

5. Making a decision: If the calculated F-value is greater than the critical value, the null hypothesis is rejected, and it can be concluded that there are significant differences between at least two group means. Conversely, if the calculated F-value is smaller than the critical value, the null hypothesis is not rejected, indicating that there is no significant difference between the group means.

If the null hypothesis is rejected, post-hoc tests can be conducted to determine which specific group means differ significantly from each other.

one-way ANOVA utilizes the five steps of hypothesis testing to determine if there are significant differences among the means of three or more groups.

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Answer:

6* 2.2lb = 13.2 lb

Step-by-step explanation:

If 1 bag weights 2.2lb than 6 bags will weight 6 times more or:
2.2 lb * 6 = 13.2 lb

We can use the provided conversion factor, which states that 1 kg is equal to 2.2 pounds, to determine the weight of the cat food in pounds.

Since each bag of cat food weighs 6 kg, we can calculate the weight of 5 bags as follows.

5 bags of 6 kg each equal the total weight = 30 kg.

Now, we can convert the total weight from kilograms to pounds using the conversion factor:

Total weight multiplied by the conversion factor equals total weight in pounds.

= 30 kg x 0.2 lb/kg.

= 66 lbs.

Consequently, the cat food has a 66-pound weight when measured in pounds.

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The z- score of a person who scored 280 on the exam can be found to be - 0. 5.

A z-score indicates how many standard deviations an element is from the mean.

The formula is:

Z = ( X - μ ) / σ

The details here are:

X = 280, μ = 300, and σ = 40

The z - score is therefore :

Z = (280 - 300) / 40

= -20 / 40

= -0.5

In conclusion, the z - score of a person who scored 280 on the exam is -0.5. This means that their score is half a standard deviation below the mean.

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Answer:

138ft^2

Step-by-step explanation:

9x2=18

10x12=120

18+120=138ft^2

Answer:

48in.²

Step-by-step explanation:

The formula for the area of a triangle is 1/2 x b x h

Since the b = 8 and the h = 12, substitute 8 and 12 for b and h.

1/2 x 8 x 12

4 x 12

48in.²

Answer:

d

Step-by-step explanation:

area= ½ × b × h

= ½ × 8 × 12

= ½ × 96

= ⁹⁶/²

= 48in²

The unknown length of the similar figure is:

x = 15 units

Two figures are similar if they have the same shape but different sizes. The corresponding angles are equal and the ratios of their corresponding sides are also equal.

Using the above concept, we can equate the ratio of the corresponding sides and solve for the unknown lengths. That is:

TV/AC = TU/AB

x/10 = 6/4

x/10 = 1.5

x = 10 * 1.5

x = 15 units

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Answer: 59,048

Step-by-step explanation:

To find the sum of the given finite series:

Σ2· (3)n-1

n=1

where n ranges from 1 to 10, we can use the formula for the sum of a geometric series.

The formula for the sum of a geometric series is:

S = a * (r^n - 1) / (r - 1)

In this case, a = 2 (the first term of the series) and r = 3 (the common ratio).

Using the formula, we can calculate the sum:

S = 2 * (3^10 - 1) / (3 - 1)

= 2 * (59049 - 1) / 2

= (118098 - 2) / 2

= 118096 / 2

= 59048

Therefore, the sum of the given finite series is 59,048.

physical sciences 2023

The value of period of function is,

Period = 2

Since, A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

We have to given that;

The graph of function is shown in figure.

Since, The distance between the repetition of any function is called the period of the function.

And, For a trigonometric function, the length of one complete cycle is called a period.

Hence, By definition of period, we get;

The value of period of function is,

Period = 3 - 1

Period = 2

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The equation that represents the total cost is C = $50 + $70t.

The total amount earned by the electrician is the sum of the fixed cost and the variable cost.

Total amount earned = fixed cost + variable cost

The fixed cost is the set fee he charges . The variable cost is a function of the additional hourly fee and the number of hours

The equation that represents the the total amount earned when he works for 5 hours is:

$400 = $50 + (5 x v)

$400 = $50 + 5v

$400 - $50 = 5v

$350 = 5v

v = $350 / 5

v = $70

C = $50 + $70t

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The conversion of 3185 degrees to minutes and seconds is 19 minutes and 6.6 seconds

From the question, we have the following parameters that can be used in our computation:

Degrees = 0.3185

By definition, there are 60 minutes in a degrees

So, we have

Minutes = 0.3185 * 60

Evaluate the product

Minutes = 19.11

The decimal part of the product above represents the number of seconds

So, we have

Minutes = 19

Seconds = .11 * 60

Evaluate

Seconds = 6.6

Hence, .3185 degrees is 19 minutes and 6.6 seconds

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Answer:  2

Step-by-step explanation:

List the factors(numbers that multiply to make that number for each number

6: 1, 2, 3, 6

34: 1, 2, 16, 34

2: 1, 2

Whichever is the factor that is the greatest that they all have in common is your greatest common factor.

2

The measure of arc angle QTP is 204 degrees.

When a tangent and a secant intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

Therefore, let's find the measure of arc angle QTP as follows:

90 = 0.5(x - 68)

90 = 0.5x - 34

0.5x = 124

x = 124 / 0.5

x = 248 degrees

Where

x = arc angle TSQ

Therefore,

arc QP = 44 degrees

Therefore,

arc QTP = 248 - 44

arc QTP = 204 degrees

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The animal that swims at a top speed of 0. 33 miles per minute would be the Dolphin .

To find the animal that swims at a top speed of 0. 33 miles per minute, you need to convert their top speeds in miles per hour to miles per minute.

For every 1 mile per hour, the equivalent in minutes is 0.0166667 miles per minute.

Speed of Swordfish is:

= 60 mph x 0.0166667

= 1 mile per minute

Speed of Tuna :

= 45 mph x 0.0166667

= 0. 75 miles per minute

Dolphin :

= 20 mph x 0.0166667

= 0. 33 miles a minute

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The domain of the function f(x) is all real numbers except x = -7. In interval notation, we can express the domain as (-∞, -7) ∪ (-7, +∞).

To find the domain of the function f(x) = (x - 3)/(x + 7), we need to determine the values of x for which the function is defined.

The function is defined for all values of x except those that make the denominator, x + 7, equal to zero.

Division by zero is undefined in mathematics.

So, we set the denominator equal to zero and solve for x:

x + 7 = 0

x = -7

Hence, the only value that makes the denominator zero is x = -7. Therefore, the domain of the function f(x) is all real numbers except x = -7.

In interval notation, we can express the domain as (-∞, -7) ∪ (-7, +∞).

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Answer:24.1104189866

Step-by-step explanation:

the answer to What is 692837 divided by 28736 is 24.1104189866

Answer:

Step-by-step explanation:

The angles in the parallel lines are solved

∠9 and ∠16 = alternative exterior angles

∠15 and ∠11 = supplementary angles

∠10 and ∠15 = alternate interior angles

∠12 and ∠15 = vertical angles

∠9 and ∠11 = corresponding angles

∠9 and ∠15 = none

∠13 and ∠14 = supplementary angles

∠14 and ∠11 = alternative interior angles

Given data ,

Let the two parallel lines be represented as a and b

where the transversal line is m

Now , from the given figure , we can deduct that

We can conclude some factors determining parallel lines ,

Alternate angles are equal

Corresponding angles are equal

Co-interior angles add up to 180°

Now , the angles are

∠9 and ∠16 = alternative exterior angles

∠15 and ∠11 = supplementary angles

∠10 and ∠15 = alternate interior angles

∠12 and ∠15 = vertical angles

∠9 and ∠11 = corresponding angles

∠9 and ∠15 = none

∠13 and ∠14 = supplementary angles

∠14 and ∠11 = alternative interior angles

Hence , the angles are solved

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The correct matching of each compound to its type:

8.1 CO - oxide

8.2 CO₂ - dioxide

8.3 SO₂ - dioxide

8.4 CaCO - incorrect notation (needs a subscript for the number of atoms)

8.5 NaOH - hydroxide

8.1 CO - oxide

8.2 CO₂ - dioxide

8.3 SO₂ - dioxide

8.4 CaCO - carbonate

8.5 NaOH - hydroxide

Here is the correct matching of each compound to its type:

8.1 CO - oxide

8.2 CO₂ - dioxide

8.3 SO₂ - dioxide

8.4 CaCO - incorrect notation (needs a subscript for the number of atoms)

8.5 NaOH - hydroxide

Compound 8.4, CaCO, is not correctly represented. It should have a subscript to indicate the number of atoms present in the compound.

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Answer: E. 25%

Step-by-step explanation: There are 12 circles in total. 3 out of those twelve are shaded in, making it in fraction form 3/12. dividing both the numerator in the denominator by 3 simplifies it into 1/4. which is subsequently, 25%

the amount of cubic feet(Volume) the tent can hold is 165 ft³.

Volume is the space occupied by an object.

To caculate the amount of cubic feet(Volume), the tent can hold, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the right option is (A) 165 ft³.

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The contrapositive of the original conditional statement is B. If a number does not have a negative cube root, then the number is not negative.

In logic, the contrapositive of a conditional statement is a logically equivalent statement that switches the positions of the hypothesis and the conclusion, while also negating both.

The contrapositive maintains the logical validity of the original statement. If the original statement is true, then the contrapositive is also true, and vice versa.  "If a number is negative, then it has a negative cube root." The contrapositive of this statement would be: "If a number does not have a negative cube root, then the number is not negative."

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Answer:

752.4

Step-by-step explanation:

Here we are provided with a decagon which has 10 sides.

The total interior angle is 360°.

So each will have 360/10 = 36 degrees

Half of that is 18 degrees inside the triangle.

Refer to the attachment below.

opposite = 16sin(18)

adjacent = 16cos(18)

Find the area of this triangle:

= 1/2 × 16sin(18) × 16cos(18)

= 37.61825

There are 20 triangles just like this so the total area is (37.61825 × 20) = 752.365 ≈ 752.4 unit2