ANSWER
[tex]S_5=91\frac{10}{81}[/tex]
EXPLANATION
The sum of the first [tex]n[/tex] terms of a geometric sequence is given by;
[tex]S_n=\frac{a_1(1-r^n)}{1-r} ,-1<\:r<\:1[/tex]
Where [tex]n[/tex], is the number of terms and [tex]a_1[/tex] is the first term.
When [tex]n=5[/tex], we have [tex]a_1=81[/tex], we get;
[tex]S_5=\frac{81(1-(\frac{1}{9})^5)}{1-\frac{1}{9}}[/tex]
[tex]S_5=\frac{81(1-\frac{1}{59049})}{1-\frac{1}{9}}[/tex]
[tex]S_5=\frac{81(\frac{59048}{59049})}{\frac{8}{9}}[/tex]
[tex]S_5=\frac{7381}{81}[/tex]
[tex]S_5=91\frac{10}{81}[/tex]
Please help! Question below (:
The 3 inside angles of a triangle need to equal 180 degrees.
You are given 28 for one.
The second on is adding 58 + 77 = 135 degrees.
X = 180 - 28 - 135 = 17 degrees
Customers at Fair Weather Farmer's Market love to sample Ava's homemade strawberry jam. A jar of jam contains 12 ounces, and the sample size is 1 2 of an ounce. How many people can sample from one jar?
It is given that the sample size is half or [tex]\frac{1}{2}[/tex] of an ounce.
It is also given that a jar of jam contains 12 ounces.
Let the number of people who sample from the jar be "x". Then it is clear that:
[tex]\frac{1}{2}\times x=12[/tex]
Therefore, we will have [tex]x=\frac{12}{\frac{1}{2}}=12\times 2=24[/tex]
Therefore, 24 customers at Fair Weather Farmer's Market who love to sample Ava's homemade strawberry jam can sample from one jar.
Please try to answer quickly thanks :)
The Distance between the 2 points is 15 units
Gia got some books from the library yesterday. She got 5 books today after returning 3. Gia now has 6 books. How many library books did gia begin with?
Answer:
4
Step-by-step explanation:
Given: Gia got some books from the library yesterday. She got 5 books today after returning 3. Gia now has 6 books.
To Find: How many library books did gia begin with.
Solution:
Let the number of library books gia begin with [tex]=\text{x}[/tex]
Number of books gia got today [tex]=5[/tex]
Number of books gia returned [tex]=3[/tex]
Total number of books Gia has [tex]=(\text{Total number of books is started with})+(\text{number of books gia got})-(\text{books gia returned})[/tex]
[tex]\text{x}+5-3[/tex]
[tex]\text{x}+2[/tex]
Total number of books gia has [tex]=6[/tex]
now,
[tex]\text{x}+2=6[/tex]
[tex]\text{x}=6-2[/tex]
[tex]\text{x}=4[/tex]
Hence number of books gia started with is 4
The number of books Gia started with is 4
Let the number of books she got yesterday = x
Total Number of books she has gotten = 6
Books she got today = 3
Number of books she returned = 5
Expressing this as an equation :
Total books gotten = (x + 5 - 3)
6 = x + 5 - 3
6 = x + 2
6 - 2 = x
x = 4
The number of books Gia started with is 4.
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What is 858 divided by 57 using partial quotients
Answer:
The answer will be: [tex]15 + \frac{3}{57}[/tex]
Step-by-step explanation:
In Partial quotients method, first we will subtract an easy multiple of the divisor from the dividend. Then repeat the subtraction until the remainder is less than the divisor. Finally, we need to add up all the multiples of the divisor to find the quotient of the division.
Here, dividend is 858 and divisor is 57.
[tex]57)\overline{858}[/tex]
- 570 × 10
288
- 285 × 5
3
So, the quotient of the division will be: [tex](10+5)=15[/tex] and the remainder is: 3
We can write the answer as: [tex]15 + \frac{3}{57}[/tex]
write all of the digita that can rwplace each 735<7 ■ 4<761
The digits 4 and 5 can replace the box in order to make the inequality true.
Any digits larger than 5 or less than 4 will not make it true.
Suppose we used 3.
735 is not greater than 734, and so the inequality would be false.
Now let's suppose we used 6.
764 is not less than 761.
A list of digits that can replace the given expressions 735<7 and 4<761 has been provided.
Explanation:The provided question asks for a list of numbers that can replace the expressions 735<7 and 4<761. To find the numbers that can replace these expressions, we need to identify the digits in the list provided that satisfy the conditions. Let's go through each digit in the list and determine if they can replace the expressions:
For 735<7, we can see that the digits 664, 695, 696, 698, 707, 712, 713, 721, 723, 725, 761, 762, 763, 767, 775, 778, 805, 833, 889, 893, 899, 903, 909, 921, and 923 are all greater than 735 and thus satisfy the condition.For 4<761, the digits 136, 140, 178, 190, 205, 215, 217, 218, 232, 234, 240, 255, 270, 275, 290, 301, 303, 315, 317, 318, 326, 333, 343, 349, 360, 369, 377, 388, 391, 392, 398, 400, 402, 405, 408, 422, 429, 450, 475, and 512 are all less than 761 and satisfy the condition.Therefore, the list of digits that can replace 735<7 are: 664, 695, 696, 698, 707, 712, 713, 721, 723, 725, 761, 762, 763, 767, 775, 778, 805, 833, 889, 893, 899, 903, 909, 921, 923. The list of digits that can replace 4<761 are: 136, 140, 178, 190, 205, 215, 217, 218, 232, 234, 240, 255, 270, 275, 290, 301, 303, 315, 317, 318, 326, 333, 343, 349, 360, 369, 377, 388, 391, 392, 398, 400, 402, 405, 408, 422, 429, 450, 475, and 512.
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The formula for the area of a triangle is A =bh/2. Solve the formula for h. (30 points)
The given formula is A= bh/2
First multiply both sides by 2:
2A = bh
Now divide both sides by b:
h = 2A/b
Eight packages of strawberries cost $24. How many packages can you buy for $12
Consider these two histograms representing two sets of data with 10 observations each. Which of the following is true?
A. The means are equal and the standard deviation of Plot 1 is smaller than the standard deviation of Plot 2.
B. The means are equal and the standard deviations are equal.
C. The mean and standard deviation of Plot 2 are larger than the mean and standard deviation of Plot 1.
D. The means are equal and the standard deviation of Plot 1 is larger than the standard deviation of Plot 2.
Answer:
The answer is D . The means are equal and the standard deviation of Plot 1 is larger than the standard deviation of Plot 2.
Step-by-step explanation:
The histogram gives you information about the number of times a specific number appears on your sample. Then you can construct your sample looking at each histogram. For example in Plot 1 the value -2 appears two times. If you this, you obtain the following samples:
Plot 1: -2, -2, -1, -1, 0, 0, 1, 1, 2, 2
Plot 2: -2, -1, -1, 0, 0, 0, 0, 1, 1, 2
If you calculate the means by adding and dividing by the number of obs you find equal means (0) because the data is centered around 0. ( no deviations to left or right).
Now the standard deviation (sd) can be infered in the histogram. The sd measures the distance around the mean of the data. When data is concentrated very close to the mean, the sd is lower as in Plot 2 (More points are 0 or around zero in Plot 2). In plot 1 your points are farther apart from the mean of zero so the sd is higher.
what is the GCF of 32 and 56
A recipe for modeling clay requires 1/3 cup of salt. how many recipes of salt can carla make with 7 3/4 cups of salt
Answer:
- The error is: [tex](\frac{31}{4})(\frac{1}{3})[/tex]
- The correct solution is: [tex]\frac{93}{4}=23^{\frac{1}{4}}[/tex] (Carla can make approximately 23 recipes with the clay).
Step-by-step explanation:
1. Carla must divide [tex]\frac{31}{4}[/tex] ÷ [tex]\frac{1}{3}[/tex] as following:
- Take the reciprocal of [tex]\frac{1}{3}[/tex].
- Multiply the numerators and the denominators.
Then:
[tex](\frac{31}{4})(\frac{1}{3})=\frac{(31)(3)}{(4)(1)}=\frac{93}{4}[/tex]
2. As a mixed number:
[tex]\frac{93}{4}=23^{\frac{1}{4}}[/tex]
3. Therefore, Carla can make approximately 23 recipes with the clay.
Carla can make 23 full modeling clay recipes with 7 3/4 cups of salt, with a quarter cup of salt remaining.
To find out how many recipes of modeling clay Carla can make with 7 3/4 cups of salt, we need to divide the total amount of salt she has by the amount required for one recipe. Since one recipe requires 1/3 cup of salt, we will perform the following division: 7 3/4 divided by 1/3.
To simplify this, first, convert 7 3/4 to an improper fraction, which is (7 × 4 + 3)/4, or 31/4. Now, dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we multiply 31/4 by the reciprocal of 1/3, which is 3/1.
31/4 × 3/1 = 93/4, which simplifies to 23 1/4.
This means Carla can make 23 full recipes with a little salt left over.
If m arc HAM = 265°, find the measure of the corresponding minor arc. circle Z with radius ZH, diameter MT, and point A opposite point H
If the major arc HAM is 265°, then the minor arc MH is: 360° - 265° = 95°
Major arc plus minor arc equals the full circle of 360°
Answer: 95°
HELP with math vocab WILL GIVE BRAINLIEST
1.
Devices, such as parentheses, brackets, and fraction bars, used to set apart an expression that should be simplified before other operations are performed
2.
An expression that consists of numbers, operations, and sometimes grouping symbol.
3.
The order in which operations must be computed when more than one operation is involve.
4.
A number representing how many times the base number should be multiplied by itself.
5.
A Symbol that represents a value that can change.
6.
A single number or variable, or numbers and variables multiplied together.
7.
The numerical factor in a term. A number being multiplied by a variable.
8.
A number on its own, it has a fixed value.
9.
A combination of variables, numbers, and operations.
10.
You replace, or substitute, all the variables with numbers and then simplify.
11.
A statement that the values of two math expressions are equal (indicated by the sign =).
12.
The relation between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
13.
The symbol of a math operation.
plus, minus, times, divided by, equals
14.
An equation or inequality containing one or more variable.
Order of Operations
Grouping Symbol
Evaluate
Exponent (Power)
Numerical Expression
Inequality
Term
Variable
Equation
Coefficient
Constant
Operator
Open Sentence
Variable Expression
Answer:
1 : Grouping Symbol
2 : Operator
3 : Order of Operations
4 : Exponent
5 : Variable
6 : Term
7 : Coefficient
8 : Constant
9 : Numerical Expression
10 : Variable Expression
11 : Equation
12 : Inequality
13 :
14 : Open Sentence
Those are the ones I know. I hope this helps
Answer:
i agree with BreezyXXX
Step-by-step explanation:
Identify the property that justifies the statement.
∠XYZ≅∠PDQ and ∠PDQ≅∠ABC, so ∠XYZ≅∠ABC.
Answer: Transitive property of Equality.
Therefore if ∠XYZ≅∠PDQ and ∠PDQ≅∠ABC then by transitive property of equality we have ∠XYZ≅∠ABC.
The law of transitivity tells that if a equals to b and b equals to c then a equals to c.
For example If Jane has same height of Susan and Susan has same height of Tina then Jane has same height of Tina.
The statement "∠XYZ ≅ ∠PDQ and ∠PDQ ≅ ∠ABC, so ∠XYZ ≅ ∠ABC" is justified by the Transitive Property of Equality, which indicates that the congruence of the first and third angle is established through their mutual congruence to the second angle.
Explanation:The property that justifies the statement "∠XYZ ≅ ∠PDQ and ∠PDQ ≅ ∠ABC, so ∠XYZ ≅ ∠ABC" is the Transitive Property of Equality. This property states that if a first thing is equal to a second thing, and the second thing is equal to a third thing, then the first thing is also equal to the third thing.
In the context of angles, if ∠XYZ is congruent to ∠PDQ, and ∠PDQ is congruent to ∠ABC, then by the Transitive Property, ∠XYZ must be congruent to ∠ABC.
If their food and beverages cost 25.30 and there is an 8% meals tax, how much is the bill?
Is (1, 6) a solution to this system of equations? Y = 9x + 10 y = x + 5
The price of a necklace was increased by 20% to ?186. What was the price before the increase?
Answer:
148.8
Step-by-step explanation:
The original price of the necklace before the 20% increase was approximately £155 (£186 / 1.20).
To find the original price of the necklace before the 20% increase, we can use the formula:
Original Price = Final Price / (1 + Percent Increase)
Given that the final price is £186 and the increase is 20%, we substitute these values into the formula:
Original Price = £186 / (1 + 0.20)
Calculating inside the parentheses first:
1 + 0.20 = 1.20
Now, divide the final price by 1.20:
Original Price = £186 / 1.20 ≈ £155
So, the original price of the necklace before the increase was approximately £155.
Please help and show work!! Timed!! Will mark brainliest!!
(3w²r)²(-2w⁵r²)³ = When a power is raised to a power the exponents have to be multiplied.
(3²w⁽²*²⁾r²)(-2³w⁽⁵*³⁾r⁽²*³⁾) = We can take out the constants
= (3²)(-2³)(w⁴r²)(w¹⁵r⁶) = We can group the same variables
= -72(w⁴w¹⁵)(r²r⁶) = When multiplying two powers that have the same base, you have to add the exponents.
= -72w⁽⁴⁺¹⁵⁾r⁽²⁺⁶⁾ = -72w¹⁹r⁸
Answer : F) -72w¹⁹r⁸
Hope this helps!
[tex]\textit{\textbf{Spymore}}[/tex]
Use the probability distribution table to answer the question.
What is P(1
ANSWER
[tex]P(1<X<5)=0.51[/tex]
EXPLANATION.
The probability of selecting a number between 1 and 5 can be calculated by summing all probabilities between 1 and 5
[tex]P(1<X<5)=P(X=2)+P(X=3)+P(X=4)[/tex]
[tex]P(1<X<5)=0.07+0.22+0.22[/tex]
[tex]P(1<X<5)=0.51[/tex]
25 POINTS! PLEASE HELP! two Algebra 2 questions!
1). What is the result of dividing 2x^3+x^2−2x+8 by x + 2?
a).2x2−3x+16
b). 2x2−3x+4
c). 2x2+5x−8
d). 2x2+5x+8
2). Noemi wants to divide 2x2−x+4 by x−5 using synthetic division.
(answer is linked with photos)
(b) 2x² - 3x + 4
using synthetic division or long division to obtain the quotient 2x² - 3x + 4
How many pounds of coffee worth $9 a pound should be added to 10 pounds of coffee worth $3 a pound to get a mixture worth $7 a pound
6-^3
------
6-^4
A) 6-7
B) 6-1
C) 61
D) 612
Answer:
[tex]6^1[/tex]
Step-by-step explanation:
[tex]Use\\\\\dfrac{a^n}{a^m}=a^{n-m}\\\\\dfrac{6^{-3}}{6^{-4}}=6^{-3-(-4)}=6^{-3+4}=6^1[/tex]
Hat is the greatest common factor of 20 and 36? 2 4 5 6
In math what does it mean by Define the varible?
Final answer:
To define the variable in mathematics means to assign symbols to represent quantities that can take various values, either as numerical variables measurable in the same units or as categorical variables for classification purposes. This allows for the exploration of relationships and predictions of outcomes.
Explanation:
In mathematics, the term 'define the variable' refers to the process of assigning a symbol, typically a letter such as X or Y, to represent a quantity that can take on various values. Variables can be of different types, such as numerical variables which represent values measurable in the same units like time in hours or weight in pounds, and categorical variables which classify individuals or items into categories, such as political affiliation.
For example, in the equation of a line y=mx+b, x and y are variables with x usually representing the independent variable plotted along the horizontal axis, and y as the dependent variable plotted on the vertical axis. The variable m represents the slope of the line, and b represents the y-intercept, or the point where the line crosses the y-axis. By defining each variable, a mathematician or an economist can explore the relationship between quantities and predict outcomes.
An example in statistics would be letting X represent the number of children in a family, making it a numerical variable, where each specific number of children would be represented by a lowercase x (0, 1, 2, 3, etc.). Conversely, if Y represents someone's political party, each category (Republican, Democrat, Independent, etc.) is an example of a categorical variable, which does not make sense to average mathematically like numerical variables.
What can the zeros and intercepts of a quadratic function tell you about real world relationships?
Suppose, we are given a function
[tex]f(x)=ax^2+bx+c[/tex]
Application of Zeros:
we know that
zeros are x-intercepts
We know that zeros are values of x for which f(x)=0
and it has very wide application
It is extremely useful in real world applications such as finance, astronomy, geology, architecture, or physics
For exp:
[tex]h(t)=-16t^2 + 96t + 112[/tex]
Zeros will help us to find time at which ball reaches to ground
so, we set h(t)=0
and then we can solve for t
value of t are zeros
Application of y-intercept:
we know that y-intercepts are values of y at which x=0
It's application can be population , finance and physics etc
For exp:
[tex]h(t)=-16t^2 + 96t + 112[/tex]
we can find initial height of object after plugging t=0
[tex]h(0)=-16(0)^2 + 96(0) + 112[/tex]
[tex]h(0)=112[/tex]
so, body dropped from 112 feet
Please help asap 27pts
[tex]7x\geq-56\qquad|\text{divide both sides by 7}\\\\x\geq-8\\-------------------------------\\9x < 54\qquad|\text{divide both sides by 9}\\\\x < 6\\\\Answer:\ d)\ -8\leq x < 6[/tex]
What are numbers that are either whole numbers or negatives of whole numbers
These are called integer numbers.
We start with natural numbers (or whole numbers), i.e. the set
[tex] \mathbb{N} = \{0,1,2,3,4,\ldots\} [/tex]
When you add the opposite of each whole number, you have the set of integers:
[tex] \mathbb{Z} = \{0,\pm1,\pm2,\pm3,\ldots\} [/tex]
Answer:the not called whole numbers there called integers
Step-by-step explanation: whole numbers are 0 1 2 3 4 and so on integers are 0 -1 -2 -3 -4 and so on
He repartido mi colección de canicas entre mis tres amigos. A tales le he dado 1/5 del total, a arquímedes 1/3 del resto, y por último, a pitágoras, le he regalado 16 canicas que me quedaban
You originally had 30 canicas in your collection.
Let's denote the total number of canicas in your collection as C
According to the information provided:
1. Tales received 1/5 of the total:
Tales received [tex]\( \frac{1}{5} \)[/tex] of C, which can be expressed as [tex]\( \frac{1}{5} \times C \).[/tex]
2. You received 1/3 of the rest:
After giving Tales his share, there are [tex]\( \frac{4}{5} \)[/tex] of the canicas left. You received [tex]\( \frac{1}{3} \)[/tex] of this remaining amount. So, your share is [tex]\( \frac{1}{3} \times \frac{4}{5} \times C \)[/tex].
3. Pitagórica received the remaining 16 canicas:
After Tales and you received your shares, Pitagórica received the remaining canicas, which is given as 16 canicas.
Now, we can set up an equation to represent this situation:
[tex]\[ \frac{1}{5} \times C + \frac{1}{3} \times \frac{4}{5} \times C + 16 = C \][/tex]
Now, let's solve for C:
[tex]\[ \frac{1}{5}C + \frac{4}{15}C + 16 = C \][/tex]
Combine the terms with C:
[tex]\[ \frac{3}{15}C + \frac{4}{15}C + 16 = C \][/tex]
Combine the terms on the left side:
[tex]\[ \frac{7}{15}C + 16 = C \][/tex]
Subtract [tex]\( \frac{7}{15}C \)[/tex] from both sides:
[tex]\[ 16 = \frac{8}{15}C \][/tex]
Now, solve for C:
[tex]\[ C = \frac{15}{8} \times 16 \][/tex]
[tex]\[ C = 30 \][/tex]
Therefore, you originally had 30 canicas in your collection.
Complete question:
He divided my collection of dogs among my three best friends. A Tales to him he gave 1/5 of the total, a Here to me 1/3 of the rest, and lastly to Pitagórica, he gave me the 16 canicles that I sobraron.
How many canicas do I have in my collection?
A moving company has a truck filled for deliveries to four different sites. If the order of the deliveries is randomly selected what is the probability that is the shortest route?
As there are 4 different sites so we have 4! possible arrangements to choose from so it becomes = [tex]4\times3\times2\times1=24[/tex]
And there will be only 1 shortest route out of these.
So the probability that the route selected is the shortest route becomes = [tex]\frac{1}{24}[/tex]
The question involves finding the probability of randomly arranging deliveries to four sites such that the arrangement corresponds to the shortest route. With 24 possible arrangements, only one of which constitutes the shortest route, the probability is 1/24.
Explanation:This question involves the concept of permutations in probability. If delivery sites are being randomly selected, there are 4! (4 factorial) possible sequences for the deliveries, i.e., 4*3*2*1 = 24 different routes.
Assuming that only one of these combinations constitutes the shortest route, the probability of randomly selecting the shortest route is therefore 1 out of 24. To obtain this, you divide the number of favorable outcomes (1 - because there's only one shortest route) by the total outcomes (24 - from 4 factorial).
So, "the probability of selecting the shortest route randomly is 1/24".
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Volunteers were 3/4 finished with the walk-a-thon when they reached 4 1/2 kilometer mark how long was the walk-a-thon in kilometers
It would be 6 km because 4 1/2 divided by 3 = 1.5x4=6