The smallest possible value of x+y+z such that 3^x+5^y+7^z is divisible by 105 is 11.
What are Natural Numbers?Natural numbers are a set of positive integers that are used for counting and ordering. In other words, natural numbers are the set of numbers that are used to represent the quantity of objects, such as 1, 2, 3, 4, 5, 6, and so on. Some definitions include zero as a natural number, while others define natural numbers to start from 1. In mathematics, natural numbers are denoted by the symbol "N" or "N+", and are sometimes referred to as counting numbers.
What are whole numbers?Whole numbers are a set of non-negative integers that include all natural numbers (positive integers) and zero. Whole numbers are used to represent quantities that cannot be divided into smaller parts, such as the number of people in a room, the number of apples in a basket, or the number of books on a shelf.
In the given question,
We know that 105 is a multiple of 3, 5, and 7. Therefore, if 3^x+5^y+7^z is divisible by 105, it must also be divisible by 3, 5, and 7.
If 3^x+5^y+7^z is divisible by 3, then 3^x ≡ 0 (mod 3), which means x ≥ 1.
If 3^x+5^y+7^z is divisible by 5, then 5^y ≡ 0 (mod 5), which means y ≥ 1.
If 3^x+5^y+7^z is divisible by 7, then 7^z ≡ 0 (mod 7), which means z ≥ 1.
Therefore, we have x+y+z ≥ 3.
We also know that 105 is the smallest multiple of 3, 5, and 7. Therefore, we want to find the smallest values of x, y, and z that will make 3^x+5^y+7^z divisible by 105.
If we want 3^x+5^y+7^z to be divisible by 105, we need x, y, and z to be multiples of 4, 4, and 3, respectively.
The smallest such values are x=4, y=4, and z=3. Therefore, the smallest possible value of x+y+z is 4+4+3=11.
So, the smallest possible value of x+y+z such that 3^x+5^y+7^z is divisible by 105 is 11.
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Suppose that a company wishes to predict sales volume based on the amount of advertising expenditures. The sales manager thinks that sales volume and advertising expenditures are modeled according to the following linear equation. Both sales volume and advertising expenditures are in thousands of dollars.
Estimated Sales Volume=45.15+0.54(Advertising Expenditures)
If the company has a target sales volume of $125,000
, how much should the sales manager allocate for advertising in the budget? Round your answer to the nearest dollar.
Answer:
We can use the given equation to solve for the advertising expenditures needed to achieve the target sales volume of $125,000:
125 = 45.15 + 0.54x
where x is the advertising expenditures in thousands of dollars.
Simplifying the equation:
0.54x = 125 - 45.15
0.54x = 79.85
x = 79.85 / 0.54
x ≈ 147.69
Therefore, the sales manager should allocate about $147,690 for advertising in the budget to achieve the target sales volume of $125,000.
Step-by-step explanation:
to make coldrink 1 must mix concentrate with water in a ratio of 1:3
if I have 400ml of concentrate how much water must I use?
Answer:
1200ml or 1.2l of water
Step-by-step explanation:
concentrate:water
1:3
400:x
3×400=1200
400:1200
1200ml or 1.2l of water
- The water level in a retention pond started at 5 ft (60 in.) and decreased at a rate of 2 in./day during a 14-day drought. A tropical depression moved through at the beginning of the 15th day and produced rain at an average rate of 2.5 in./day for 5 days. Write a piecewise-defined function to model the water level L (x) (in inches) as a function of the number of days x since the beginning of the drought.
The piecewise function that models model the water level L (x) (in inches) as a function of the number of days x since the beginning of the drought is given as follows:
L(x) = 60 - 2x, 0 ≤ x ≤ 14.L(x) = 30 + 5x, 15 ≤ x ≤ 19.How to define a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which;
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.A piecewise function is a function with different definitions, based on the input of the function.
For the first 14 days, the parameters are given as follows:
b = 60 -> water level during day 0.m = -2 -> each day the amount decreased by 2 in.Hence:
L(x) = 60 - 2x, 0 ≤ x ≤ 14.
For the last 5 days, the parameters are obtained as follows:
b = 60 - 2(15) = 30.m = 5, as each day the amount increased by 2 in.Hence:
L(x) = 30 + 5x, 15 ≤ x ≤ 19.
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Select the equation that is true. A. 2 2 3 × 4 = 8 2 3 B. 2 2 3 × 5 8 = 1 2 3 C. 2 2 3 × 2 3 = 2 4 9 D. 2 2 3 × 4 3 5 = 8 6 15 its fractions im lazy thats all
The equation 2 2/3 × 2/3 = 2 4/9 is true.
What are fractions?A fraction represents a part of a whole or a ratio between two quantities. It is written as a/b, where "a" is the numerator and "b" is the denominator. The numerator represents the number of parts being considered, while the denominator represents the total number of parts in the whole or the ratio.
The equation that is true is:
C. 2 2/3 × 2/3 = 2 4/9
To solve the problem, we can convert the mixed numbers to improper fractions, and then multiply:
2 2/3 = 8/3
2/3 = 2/3
8/3 × 2/3 = 16/9
We can then convert the improper fraction back to a mixed number:
16/9 = 1 7/9
Therefore, the equation 2 2/3 × 2/3 = 2 4/9 is true.
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Pictures are the questions.
The answer to the probabilities are: (a) 0.8, (b) 0.2 (c) 0.3 (d) 0.7
What is probability?Probability is a branch of mathematics used to measure how likely something is to happen. It is calculated by taking into account the chance that a given event will occur, as well as taking into account an exhaustive set of equally likely outcomes
The percentage of married women is 80%
the number of women is 10
The probability that all of them dislike their mother in-laws is
P(x) = Number of required outcome/Number of possible outcomes
80/100 * 10 = 8 women
a) P(All of them dislike their mother in-law is 8/10 = 0.8
b) P(none of them dislike their mother-in-law is
P(x) = 1 0.8 = 0.2
c) P(At least eight of them dislike their mother-in-law)
P(x) = 8, 9, 10 = 3
Therefore, the probability is 3/10 = 0.3
d) P(no more than seven dislike their mother in-law
1,2,3,4,5,6,7 = 7
P(x) = 7/10 = .0.7
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Cera and Bethany save money using savings accounts
opened on the same day. Both deposit $20 to start and an
additional $15 each week. The graph represents the total
amount, y, in each savings account after x weeks. Describe
the number of solutions modeled in the graph and what it
means for the situation. How can you change the situation
so that the graphs model a different number of solutions?
Explain your reasoning
This could result in one, two, or multiple points of intersection, depending on the specific values of the deposits and the rates of increase.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
we can assume that the graph of Cera's and Bethany's savings accounts will show the total amount of money in their accounts after a certain number of weeks.
Since both Cera and Bethany deposit the same amount of money and make the same additional deposits each week, their savings will increase at the same rate. Therefore, the graph will likely show two parallel lines that start at $20 and increase by $15 per week.
The number of solutions modeled by the graph will depend on whether the two lines ever intersect. If the lines do not intersect, then there is no solution to the system of equations that model the two savings accounts. In other words, there is no point at which the total amount of money in both accounts is the same.
On the other hand, if the lines do intersect, then there is at least one solution to the system of equations. In this case, the point of intersection represents the week at which the total amount of money in both accounts is the same.
To change the situation so that the graphs model a different number of solutions, we could change the initial deposit or the amount of money deposited each week for one or both of the savings accounts. For example, if Cera starts with a higher initial deposit than Bethany, or if Cera deposits more money each week, then their savings will increase at different rates and the lines on the graph will not be parallel.
Therefore, This could result in one, two, or multiple points of intersection, depending on the specific values of the deposits and the rates of increase.
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tommmy earns $140 in interest after 5 years on a pricipal of $400 jane earned $132 after 4 years on principal of $600 use the intrest rate to justify which bank would you rather use tommys or janes
Comparing the interest rates of Jane and Tommy, we can say that Tommy's bank is better because he earns more amount of money for less principal amount.
What is meant by the interest rate?The amount that the lender charges the borrower over and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money.
The total interest on a loaned or borrowed sum is determined by the principal amount, the interest rate, the frequency of compounding, and the period of time the loan, deposit, or borrowing took place.
Given,
Interest earned by Tommy SI = $140
Time t = 5 years
Principal amount P = $400
Interest earned by Jane SI = $132
Time t = 4 years
Principal amount P = $600
Simple interest SI = (P × r × t)/100
where r = interest rate
For Tommy,
140 = ( 400 × r × 5) /100
r = 7%
For Jane,
132 = ( 600 × r × 4) / 100
r = 5.5%
Therefore comparing the interest rates of Jane and Tommy, we can say that Tommy's bank is better because he earns more amount of money for the less principal amount.
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A field is in the shape of a square. The length of the field is 5x³y5. What is
the area of the field terms of x and y?
Answer: The area of a square is given by the formula A = s^2, where s is the length of a side of the square.
In this case, the length of the field is 5x³y5, so each side of the square is also 5x³y5. Therefore, the area of the square can be found as:
A = (5x³y5)^2
A = 25x^6y^10
So the area of the field in terms of x and y is 25x^6y^10.
Step-by-step explanation:
8.) SAT CORNER: Gatsby leaves his dock and takes his
motorboat due east for 0.5 miles to pick up Daisy. Then,
they motor 1.2 miles north to a private island in the
middle of the sound. What is the straight-line distance,
in miles, from the island to Gatsby's dock?
The distance from the island to Gatsby's dock is 1.3 miles.
What is a Pythagoras theorem?A Pythagoras theorem is a principle that can be used to determine the unknown side of a right angled triangle when the other two sides are known.
Applying the Pythagoras theorem to the given question, let the distance from island to Gatsby's dock be represented by s. Then;
/Hyp/^2 = /Opp/^2 + /Adj/^2
s^2 = 1.2^2 + 0.5^2
= 1.44 + 0.25
= 1.69
s = 1.69^1/2
= 1.3
Thus, the straight-line distance from the island to Gatsby's dock is 1.3 miles.
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What is the inequality shown?
-6
-3 -2
-4
-5
-1
0
1
2
3 4
15
5
916
From the image given, inequality is -2≤x<8 from x≥-2, x<8. It serves as a concrete example of inequality.
What is inequality?Broadly speaking, a mathematical phrase that defines an order relationship between two integers equivalent algebraic expressions, showing whether one is bigger than, equal to, smaller than, or smaller than and equal to the other.
The sentence "5x - 4 > 2x + 3" seems like an equation because the mathematical sign for "equals" has indeed been replaced by an arrowhead. It serves as a concrete example of inequality. From the image given, inequality is -2≤x<8 from x≥-2, x<8.
Therefore, from the image given, inequality is -2≤x<8 from x≥-2, x<8.
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Elsa menabung uang di bank sebesar Rp.2.000.000,00. Apabila ia mendapat bunga 0,5% perbulan, berapa jumlah uang tabungan di bank selama 10 bulan?
Answer:
Jumlah uang tabungan Elsa setiap bulan dapat dihitung dengan rumus:
A = P(1 + r)^n
dimana:
A = jumlah uang tabungan akhir
P = jumlah uang tabungan awal
r = tingkat bunga per bulan (dalam desimal)
n = jumlah bulan
Dalam kasus ini, P = Rp.2.000.000,00, r = 0,5% atau 0,005 per bulan, dan n = 10 bulan.
Maka,
A = 2.000.000(1 + 0,005)^10
= 2.000.000(1,005)^10
= 2.000.000(1,0512)
= Rp.2.102.400,00
Jadi, jumlah uang tabungan Elsa di bank setelah 10 bulan adalah Rp.2.102.400,00.
Step-by-step explanation:
Can someone answer this just read the picture? Right answers only please!
Answer:
8,192
Step-by-step explanation:
20/100*80 =16 apply tjis in every step as they asked 4 times
Someone help me with these 3 math problems.
1. The value of the variable 'x' is 10 that is written as x = 10.
2. The equation is ∠3 + ∠4 = 90°. Then angles ∠3 and ∠4 will be complementary angles.
3. The measure of angle ∠2 is 60° which is an acute angle.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
1. ∠1 = 6x + 45 and ∠3 = 9x + 15
Angle ∠1 and angle ∠3 are opposite angles. Then the equation is given as,
∠1 = ∠3
9x + 15 = 6x + 45
9x - 6x = 45 - 15
3x = 30
x = 30 / 3
x = 10
2. Angle ∠2, angle ∠3, and angle ∠4 are supplementary angles. Then the equation is given as,
∠2 + ∠3 + ∠4 = 180°
90° + ∠3 + ∠4 = 180°
∠3 + ∠4 = 90°
3. Angle ∠1 is 120°, then the measure of angle ∠2 is given as,
∠1 + ∠2 = 180°
120° + ∠2 = 180°
∠2 = 60° (acute)
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w is less than 7 and greater than or equal to -5 write the following as an inequality
The equation y = 19(1.057) represents book sales in billions of dollars since 1990. Let x represent the number of years. Let x = 0 represent book sales in 1990. What were the total sales, in billions of dollars, in 1990? O 18 19 O 20 O 21 B 7 8. 9 10 Next
In 1990, 19 billion dollars worth of books were sold.
What is the formula for exponential growth and exponential decaying function?The formula for exponential growth is [tex]y = y_0e^{(kt)}.[/tex]
The formula for exponential decay is [tex]y = y_0e^{(-kt)}.[/tex]
We know a function is called an exponential function when the independent variable is the exponent.
An example of an exponential function is, aˣ.
Given, The equation y = 19(1.057) represents book sales in billions of dollars since 1990.
The equation is, y = 19(1.057)ˣ, Where x = the number of years.
Therefore, At x = 0 or in 1990,
y = 19(1.057)⁰.
y = 19(1).
y = 19 billion dollars
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2 the length of a rectangular picture frame is 3 inches shorter than its width if the perimeter of the picture frame is 38 inches what is the length i and width w of the frame write and solve an equation to model the problem explain the meaning of the solution
Answer:
Step-by-step explanation:
The length of a rectangular picture frame is 3 inches longer than it's width. If the perimeter of the picture frame is 38 Inches, what is the length and width ?
Given :
Perimeter of rectangle is 38 Inches
lenght is 3 inches more than the breadth.
let, width be x, and length be x+3
So, Breadth is 8 inches and length is 8+3= 11 inches.
Let's verify ::
Thus Solved !!
The ice cream above is going to melt.
When it does, will it fit in the cone or
will it overflow? Explain.
The spherical ice cream scoop and the
right cone have a radius of 3 cm.
The height of the cone is 7 cm.
Show all your work.
Answer:
well...it depends how much ice cream ia in the cone...if its 3 or more it Will definently overflow.
A community theater held auditions for their summer musical. There were 42 performers accepted in the cast. That was 60% of all those who auditioned. How many people auditioned for the musical?
Answer:
64 people
Step-by-step explanation:
I'm not so sure but I think its right.
Here's how I figured it out:
60x2=120
42x2=84
120-20=100%
84-20=64
What is $54.28 rounded to the nearest 10 dollars?
$54.28 rounded to the nearest 10 dollars is $50.00
I really need help with this
The prove that triangle ABE is congruent to triangle CDE is given below
What is congruence?Generally, To prove that triangle ABE is congruent to triangle CDE, we need to show that they have the same size and shape.
First, we can see that angle AED and angle CEB are opposite angles and therefore congruent, since AB || DC.
Also, since line AB = line DC, we know that segment AE is congruent to segment CE and segment BE is congruent to segment DE.
Using these congruent sides and the congruent angle, we can apply the Side-Angle-Side (SAS) congruence criterion to conclude that triangle ABE is congruent to triangle CDE.
Therefore, we have proven that triangle ABE is congruent to triangle CDE.
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In a population of mendel's garden peas, the frequency of dominant yellow-flowered plants is 50%. The population is in hardy-weinberg equilibrium. What is the frequency of the recessive allele in the population?.
Answer:
the frequency of the recessive allele in the population is 0.5 or 50%.
Step-by-step explanation:
In a population in Hardy-Weinberg equilibrium, the frequency of alleles remains constant from generation to generation. According to the Hardy-Weinberg law, if p is the frequency of the dominant allele and q is the frequency of the recessive allele, then:
p + q = 1
and
p^2 + 2pq + q^2 = 1
where p^2 represents the frequency of homozygous dominant individuals, 2pq represents the frequency of heterozygous individuals, and q^2 represents the frequency of homozygous recessive individuals.
Given that the frequency of dominant yellow-flowered plants is 50%, or 0.5, we can assume that p = 0.5. Substituting into the first equation, we get:
0.5 + q = 1
Solving for q, we get:
q = 1 - 0.5
q = 0.5
Therefore, the frequency of the recessive allele in the population is 0.5 or 50%.
1. Rectangle EFGH with vertices E(1,-1), F(4, -1), G(4,-5),
and H(1, -5); scale factor: k = 3,
center of dilation: (2, -4)
Answer:
The new vertices of the rectangle after applying a scale factor of 3 with a center of dilation at (2, -4) are E'(-1, -11), F'(7, -11), G'(7, -15), and H'(-1, -15
Step-by-step explanation:
Super Scary Circles Test #10
This figure is NOT drawn to scale.
a = 90°
b = 12°
C =
d =
e=
f=
g=
h=
i =
j=
Can anyone pls help me with this . We are solving for the angles and I need this done tmr .
The measures of the angles obtained using circle theorems are presented as follows;
a = 90°, b = 12°, c = 64°, d = 54°, e = 54°, f = 48°, g = 66°, h = 32°, i = 36°, and j = 20°
What are circle theorems?Circle theorems are theorems that indicates the relationships between angles, sector, chords, and tangent in a circle.
Please find the possible drawing in the question created with MS Word
a + a = 2·a = 180° (Linear pair angles)
a = 180°/2 = 90°
a = 90°
The right triangle with the acute angle angle of 78° indicates;
b = 90° - 78° = 12°
b = 12°
The angle at the center theorem indicates that we get;
The base angle of the large isosceles triangle = 2 × 32° = 64°
∠c is a base angle of the large triangle, therefore;
c = 64°
2·c + d = 180°
d = 180° - 2 × 48° = 54°
e = d = 54°
e = 54°
The angle at the circumference of the circle with angle ∠g and and ∠f = 4·b
Angle at the circumference = 4 × 12° = 48° = ∠f
f = 48°
Angle ∠g is equivalent to a base angle of the isosceles triangle, therefore;
∠g = (180° - 48°)/2 = 66°
g = 66°
Angle at the vertex of the triangle with angle h is equivalent to the base angle of the large triangle, therefore;
2·h = 64°
h = 64°/2 = 32°
h = 32°
Angle at the center = 2 × (180° - 2 × 48°) = 168°
5b + 2f + i + 168° = 360° (Angle sum property of a quadrilateral)
i = 360° - (5b + 2f + i + 168)
i = (360 - (5×12 + 2×48 + 168) = 36
i = 36
5b + 2h + i + j = 180
j = 180 - (5b + 2h + i)
j = 180 - (5 × 12 + 2 × 32 + 36) = 20°
j = 20°
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1. Amy wants to her ice cream cone filled exactly to the top. The radius of the cone is 2 in. and the height is 6 in. How much ice cream will it take to fill the cone?
2. Jack is going to fill his beach ball with water. The radius of the ball is 24 in. How much water will it take to fill the beach ball?
3. Mary is sending her sister as summer camp a square box filled with tiny candies. The side of the box measures 6 in. How much candy will it take to fill the box?
4. Jim and Mary are competing in a math contest. They have to calculate how much it takes to completely fill a canister with a radius of 4 in. and a height of 5 in. with flour. How much flour will it take to fill the canister?
5. Aunt Lillian needs to fill a shoebox with packing material. The box measured 9 in by 5 in by 5 in. How much packing material does she need to fill the box?
(It doesn’t matter what the size, the formula stays the same….)\
PLEEAAASEEE HELLLP
1. The volume of a cone is 8π cubic inches.
2. The volume of a sphere is 8π cubic inches.
3. The volume of a cube is 8π cubic inches.
4. The volume of a cylinder is 8π cubic inches.
5. The volume of a rectangular prism is 8π cubic inches.
What is volume?The volume of a thing is the area that it occupies in three dimensions. Space is what a thing occupies, to put it simply.
1. The volume of a cone is given by V = (1/3)πr²h, where r is the radius and h is the height. Substituting the given values, we get V = (1/3)π(2²)(6) = (4/3)π(6) = 8π cubic inches.
2. The volume of a sphere is given by V = (4/3)πr³, where r is the radius. Substituting the given value, we get V = (4/3)π(24³) = 18432π cubic inches.
3. The volume of a cube is given by V = s³, where s is the side length. Substituting the given value, we get V = 6³ = 216 cubic inches.
4. The volume of a cylinder is given by V = πr²h, where r is the radius and h is the height. Substituting the given values, we get V = π(4²)(5) = 80π cubic inches.
5. The volume of a rectangular prism is given by V = lwh, where l, w, and h are the length, width, and height, respectively. Substituting the given values, we get V = (9)(5)(5) = 225 cubic inches.
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Daniel already snacked on a almonds. Then he snacked on another 8 almonds. Write an expression that shows how many almonds Daniel snacked on in all.
a + 8. This expression represents the total number of almonds that Daniel snacked on in all.
What is the difference between expression and equation?
An expression is a mathematical phrase that contains numbers, variables, and operations. It can be evaluated to produce a single numerical value or another expression. Expressions do not contain an equal sign (=), and they do not represent a statement that is either true or false.
An equation, on the other hand, is a mathematical statement that shows the equality between two expressions. It contains an equal sign (=) and represents a statement that is either true or false. Equations typically contain variables that can take on different values, and they can be used to solve for an unknown variable by manipulating the equation using algebraic operations.
To summarize, expressions are mathematical phrases that do not contain an equal sign and can be evaluated to produce a value, while equations are mathematical statements that do contain an equal sign and represent a relationship between two expressions that is either true or false.
We can use addition to represent the total number of almonds that Daniel snacked on. If Daniel snacked on an initial amount of almonds, say "a", and then snacked on an additional 8 almonds, we can write the expression:
a + 8
This expression represents the total number of almonds that Daniel snacked on in all.
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The quadrants go in counter-clockwise position.
O True
O False
Answer:true
Step-by-step explanation:
A spice box manufacturing company is having difficulty filling packets to the required 50 grams. Suppose a business researcher randomly selects 60 boxes, weighs each of them and computes its mean. By chance, the researcher selects packets that have been filled adequately and that is how he gets the mean weight of 50 g, which falls in the "fail to reject" region.
The decision is to fail to reject the null hypothesis even though population mean is NOT actually 50 g.
Which kind of error has the researcher done in this case?
Answer: The researcher has made a Type II error in this case.
A Type II error occurs when the null hypothesis is not rejected even though it is false, i.e., the researcher fails to detect a significant difference when one actually exists. In this case, the null hypothesis is that the mean weight of the spice packets is 50 g, and the researcher has failed to reject this null hypothesis based on the sample mean of 50 g.
However, the population mean is not actually 50 g, and the researcher has made an error in failing to detect this difference. The sample size of 60 boxes may not have been large enough to detect a significant difference, or there may have been other factors that affected the measurements.
Therefore, the researcher has made a Type II error in this case by failing to reject the null hypothesis when it is actually false.
Step-by-step explanation:
A cube has a length of 12 cm , what is its surface area?
72 sq. cm
1500 cubic cm
1728 sq cm
864 sq. cm
Answer:
864 sq cm
Step-by-step explanation:
Surface area of cube = 6 × (l)square units. = 6 × 12cm × 12cm = 6 × 144cm = 864cmsquare.
How can i simplify 1½-⅓÷⅔+1
Answer:
2
Step-by-step explanation:
you first follow the BODMAS law then you divide 1/3÷2/3 It will give you 1/2 so you 3/2-1/2 +1 it will give you 2
can someone tell me the answers to b. and c.
1. The Range of Elevation for Long beach is 367 feet.
2. The Range of Elevation for New Orleans is 33 feet.
3. New Orleans have the average of 2 feet below sea.
What is Range?In statistics, the range is the difference between the highest and lowest values for a given data collection.
Given:
1. The Range of Elevation for Long beach
= Highest - Lowest
= 360 - (-7)
= 360 + 7
= 367 feet
2. The Range of Elevation for New Orleans
= Highest - Lowest
= 25- (-8)
= 25+ 8
= 33 feet
3. New Orleans have the average of 2 feet below sea.
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