Omar ran 950 meters farther than Paula. Option A is correct.
The total number of centimeters they both ran is 745000 centimeters. Option D is correct.
How do we determine the distance between two objects?The distance between two objects can be determined by finding their difference.
From the given information:
Paula ran 3 1/4 kilometersOmar ran 4200 metersThe way to solve this is by converting all the distances to meters.
Paula = 3250 metersOmar = 4200 metersDifference in their distance = (4200 - 3250) metersDifference in their distance = 950 meters.The total number of centimeters they both ran is:
= (420000+325000) centimeters
= 745,000 centimeters
Therefore, we can conclude that Omar ran 950 meters farther than Paula. The total number of centimeters they both ran is 745000 centimeters.
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Answer:
Omar ran 950 meters farther than Paula. Option A is correct.
The total number of centimeters they both ran is 745000 centimeters. Option D is correct.
How do we determine the distance between two objects?
The distance between two objects can be determined by finding their difference.
From the given information:
Paula ran 3 1/4 kilometers
Omar ran 4200 meters
The way to solve this is by converting all the distances to meters.
Paula = 3250 meters
Omar = 4200 meters
Difference in their distance = (4200 - 3250) meters
Difference in their distance = 950 meters.
The total number of centimeters they both ran is:
= (420000+325000) centimeters
= 745,000 centimeters
Therefore, we can conclude that Omar ran 950 meters farther than Paula. The total number of centimeters they both ran is 745000 centimeters.
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Step-by-step explanation:
Solve for p: -3p + 2 > 5
To solve these types of problems:
⇒ just solve like a regular algebraic equation
⇒ with an inequality sign in the middle
Let's solve:
[tex]-3p + 2 > 5\\-3p > 3[/tex]
whenever there is any division/multiplication⇒ must change the inequality sign to face the other direction
[tex]-3p > 3\\p < -1[/tex]
Answer: p < -1
Hope that helps!
Answer:
p < -1
Step-by-step explanation:
-3p + 2 > 5
subtract 2 from both sides
-3p + 2 - 2 > 5 - 2
-3p > 3
divided both sides by -3 to get p alone
-3p / -3 > 3 / -3 reverse the inequality
p > -1
5. Sabrina put $3,000 into a Money Market (high-yield savings)
account with an interest rate of 2.6% compounded quarterly.
a. Write an equation to model the amount in the account over
time.
b. Assuming no deposits or withdrawals are made, how much
money would be in the account after 15 years? Show your
calculation.
c. How would this problem be different if it was compounded
"continuously" instead? Calculate the amount after 15 years.
d. Name 2 or more other situations (other than a savings
account) where you might encounter compound interest later in
your life.
let me answer the last one first
compound interest is just an exponential sequence really, where the next value is some exponential amount of the previous.
hmmm that can happen in say, a bouncing ball, the 1st bounce is high, let it keep on boucing by itself and the next bounce is usually a compounded value of the previous one, since it's smaller it'd be a Decay type of equation.
hmmm it also happens in say population growth, of any organism, humans, bees, amoebas.
now let's do the others
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 2.6\%\to \frac{2.6}{100}\dotfill &0.026\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years \end{cases} \\\\\\ A=3000\left(1+\frac{0.026}{4}\right)^{4\cdot t}\implies \boxed{A=3000(1.0065)^t} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{after 15 years}}{t=15}\hspace{5em} A=3000(1.0065)^{15}\implies A\approx 3306.19 \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$3000\\ r=rate\to 2.6\%\to \frac{2.6}{100}\dotfill &0.026\\ t=years\dotfill &15 \end{cases} \\\\\\ A=3000e^{0.026\cdot 15}\implies A=3000e^{0.39}\implies A\approx 4430.94[/tex]
Which of the following functions has a maximum y-value of 2?
y = 2(x + 1)² +3
y = 3(x + 1)² +2
O y=-3(x + 1)² + 2
Oy=-(x - 2)² + 3
Answer:
-3(x+1)² + 2
Step-by-step explanation:
-3(x+1)² + 2 because the +2 indicates the y value of the turning point and the turning point is a maximum meaning the coefficient must be negative leaving this answer
Find the greatest common factor of 6m² and 7m².
Answer:
your answer is 4 my friend
Step-by-step explanation:
Determinar cuales de las siguientes frases son proposiciones
a) 3+2 = 0 c) ¡Hola!
b) x + 1 = 4 d) Yo estudio
The exercise is designed to test the students knowledge of prepositions. The correct answer thus is (Option D) Yo estudio (which translates) "I study".
What is the explanation for the answer above?To understand the answer, you need to know what a preposition is. A preposition, in simple terms, is a word or group of words that comes before a noun.
The function of a preposition (much like an adjective) is to give clarity to the noun that it precedes.
Let us complete the Preposition phrase to give meaning to it:
"I study Mathematics". Where;
"Mathematics" is the noun;
"I Study" is the prepositional phrase. Hence the correction answer to the question above is Option D.
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The ratio of black bags to blue bags is 5to 3 if there are a total of 10 black bags ,then how many blue bags are there
Answer:
6
Step-by-step explanation:
We can think of the 10 black bags as 2 sets of 5-black bags (10 divided into groups of 5; 10 / 5 ; is 2 groups/sets). So, we would also have two sets of 3 (3 x 2 = 6), or 6 bags.
5 : 3 = 10 : 6
(multiply both numbers by 2)
if x=2, and y=-3, then xy^2 =
Answer:
36
Step-by-step explanation:
If x = 2 and y = -3...
xy^2=
(2)(-3)^2 =
-6^2 =
36
XY times 2=
(-6)(2) =
-12
Answer:
18
Step-by-step explanation:
First you must fill input the values into their variable counterparts:
xy^2 turns into: 2 * -3 ^2
Since there isn't a parenthesis around x AND y, the exponent only applies to the y value.
-3 ^2 = 9, so 2 x 9 = 18
xy^2 = 18 if x =2 and y = -3
Find the solution set for |2x-3|=9
Answer:
x = 6, -3
Step-by-step explanation:
. . . . . . . . . . . . . . . . .
1) Which is the first INCORRECT step in the
solution of the inequality shown below?
2(x+1)-(3-x) ≤ -4:
Step 1: 2x + 2-3+x≤-4;
Step 2: 3x - 1≤-4;
Step 3: 3x
-3;
Step 4: x>-1
(a) Step 1
(b) Step 2
(c) Step 3
(d) Step 4
Step-by-step explanation:
we are missing the inequality sign in step 3.
step 1 and step 2 are correct.
step 4 is wrong.
the correct step 3 looks like
3x <= -3
if your original step 3 says the same, then the first wrong step is step 4.
if your original step 3 does not say the same, then the first wrong step is step 3.
Which of the following theorems verifies that AKML AOPQ?
The theorem that verifies that the two right angled triangles are similar is HA.
What are similar triangle?Two triangles are said to be similar if the ratio of their corresponding sides and the corresponding angles are equal.
Analysis:
From the diagrams KL = OQ ( hypotenuse)
∠L is equal to ∠Q which are acute.
so the two triangles are similar in hypotenuse and acute angle which is the HA theorem.
In conclusion, the HA theorem verifies that the two triangles are similar.
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²-6x +10 is to be written in the form (x-p)² +g. Find the values of p and q.
Answer:
[tex]p = 3\\\\q= 1[/tex]
Step-by-step explanation:
[tex]x^2 -6x +10\\\\=x^2 -2 \cdot 3x +3^2 -3^2 +10\\\\=(x-3)^2 -9+10\\\\=(x-3)^2 +1\\\\\text{By comparing with}~ (x-p)^2 +q, \\\\p = 3\\\\q = 1[/tex]
lanetterisbelle
6 minutes ago
Mathematics
College
Use the following information for Excercise 2-9 through Excercise 2-12 below. (Staic)
Following are the transactions of a new company called Pose-for-pics.
August 1 M. Harris, the owner, invested $6,500 cash and 33,500 of photography equipment in the company.
August 2 The company paid 2,100 cash for an insurance policy covering the next 24 months.
Aust 5 The company purchased supplies for 800 cash.
August 20 The company received 3,331 cash from taking photos for customers.
August 20 The company received 3,331 cash from taking photos for cusotmers.
August 31 The company paid $ 675 cash for August utilities.
Excercise 2-11 ( Static) Analyzing transacctions using accounting equation LO A1
Analyze each transaction above by showing its effects on the accounting equation-specifically, identify the accounts and amounts ( including + or -) Use the following partial chart of accounts: Cash; Supplies; Prepaid Insurance; Equipment; M. Harris, Capital; Services Revenue; and Utilities Expense
Date Assets = Liabilities + Equity
August 1 = +
August 1 = +
August 2 = +
August 2 = +
August 5 = +
August 5 = +
August 20 = +
August 31 Cash (+) increase 6,500 = +
Each transaction has been an analyzed in the trial balance below by showing its effects on the accounting equation-specifically, identifying the accounts and amounts.
How to prepare a Trial Balance?
The Journal Entries are:
Cash 6500
Photography equipment 33500
Capital 40000
Prepaid Insurance 2100
Cash 2100
Office Supplies 880
Cash 880
Cash 3331
Revenue 3331
Utilities Expense 675
Cash 675
Cash account = 6500 - 2100 - 880 + 3331 - 675
Cash Account = 6176
Trial Balance
Debit Credit
Cash 6176
Prepaid Insurance 2100
Supplies 880
Revenue 3331
Utilities Expense 675
Capital 40000
Photography Equipment 33500
Total 43331 43331
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Two balls are drawn without replacement from a box containing 2black and 3 red balls. What is the probability of drawing a black ball on the second draw? Draw a tree diagram
The probability of drawing a black ball on the second draw will be 3/5.
How to solve the probability?From the information given, the total number of balls will be:
= 2 + 3 = 5 balls.
When the first ball is black and the second is red. This will be:
= 2/5 × 3/4
= 3/10
When the first is red and the second is black, this will be:
= 3/5 × 2/4
= 3/10
Therefore, the probability of drawing a black ball on the second draw will be:
= 3/10 + 3/10
= 3/5.
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(a) If cos² (34°) - sin² (34°) = cos(A°),then
A =
degree’s
[tex]~~~~~~~\cos^2 \left(34^{\circ}\right) - \sin^2 \left( 34^{\circ} \right)=\cos A\\\\\implies \cos \left( 2 \cdot 34^{\circ} \right) = \cos A~~~~~~~~~~~~~;[\cos 2x = \cos^2 x -\sin^2 x]\\\\\implies \cos \left(68^{\circ}\right) = \cos A\\\\\implies A = 68^{\circ}[/tex]
Help!!!!! Meeee!! Asappppp
Reason:
Refer to the diagram below. The tiny square angle markers tell us we have a 90 degree angle, meaning those lines are perpendicular.
You can think of the parallel lines being the metal part of train tracks, while the perpendicular line connecting the metal rails is the wooden part of the train tracks.
What property states that changing the order of two or more terms does what to the value of the sum
Answer: Commutative property
45 Points!
The moon forms a right triangle with the Earth and the Sun during one of its phases, as shown below.
A scientist measures the angle x and the distance y between the Earth and the Sun. Using complete sentences, explain how the scientist can use only these two measurements to calculate the distance between the moon and
the Sun.
Answer:
by using pythagoras theorem
Step-by-step explanation:
the distance between sun and moon is hypoteneous
the distance between earth and sun is perpndicular
and distance between earth and moon is base
we can use,
tanx°=distance betwwen earth and sun/ distance betweenearth and moon
or,
sinx°= distance between earth and sun/ distance between sun and moon
we can use other formulas also same as above 2 examples
Hope ithelps
Answer:
The scientist can use trigonometry to figure out the distance between the Moon and Sun. More specifically, using sine (sin).
Step-by-step explanation:
Label the triangle first.
- x should be theta
- y would be opposite (o) as it is across/opposite from the side where x is
- the distance between the sun and moon would be hypotenuse (h), as it's opposite of the right angle.
The calculation that has o and h in it's formula is sine. The formula looks like :
Sin(Ф) = [tex]\frac{o}{h}[/tex]
To solve for the distance between the Sun and Moon, we plug it into the formula and solve
Sin(x) = [tex]\frac{d}{y}[/tex]
- where d is the distance between the Sun and Moon
hope this helps !! :D
Yolanda saves all the money from a regular baby-sitting job. The money in her savings account is increasing according to the equation y = 6x + 50, where x = number of hours worked and y = savings in dollars. Which table of values matches this equation?
Answer:
Table D
Step-by-step explanation:
I have all of the tables listed below and the correct one circled! I used to tutor my cousin about this topic!
I hope this helps and please feel free to comment, ask questions, give feedback, and correct me if I am wrong!
Have a great day!
:)
The 4th table in the option is the correct one.
What is an equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, Yolanda saves all the money from a regular baby-sitting job. The money in her savings account is increasing according to the equation y = 6x + 50, where x = number of hours worked and y = savings in dollars.
The given equation is y = 6x + 50
Put x = 0
y = 50
Put x = 5
y = 80
Put x = 10
y = 110
Put x = 15
y = 140
Creating the table,
x y
0 50
5 80
10 110
15 140
Hence, we get the table.
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Let a and ß be first quadrant angles with cos(a)=
√11/7
and sin(B)=
√11/4
Find cos(a+B)
Since both α and β are in the first quadrant, we know each of cos(α), sin(α), cos(β), and sin(β) are positive. So when we invoke the Pythagorean identity,
sin²(x) + cos²(x) = 1
we always take the positive square root when solving for either sin(x) or cos(x).
Given that cos(α) = √11/7 and sin(β) = √11/4, we find
sin(α) = √(1 - cos²(α)) = √38/7
cos(β) = √(1 - sin²(β)) = √5/4
Now, recall the sum identity for cosine,
cos(x + y) = cos(x) cos(y) - sin(x) sin(y)
It follows that
cos(α + β) = √11/7 × √5/4 - √38/7 × √11/4 = (√55 - √418)/28
Apply the indicated operations to the matrix; then choose the correct answer.
Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The correct option is B.
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
When the indicated operation 4R₁ → R₁ is applied then the matrix will be,
[tex]\left[\begin{array}{ccc}1&2&0\\-2&-1&3\end{array}\right] \rightarrow \left[\begin{array}{ccc}4&8&0\\-2&-1&3\end{array}\right][/tex]
Hence, the correct option is B.
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Gray can ride his bike 6miles in 20 minutes at this rate how many miles can he ride in 100 minutes
Forming quadratic expression.Two consecutive odd numbers are such that their product is 35.find the numbers
Answer:
Numbers are 5 , 7
Step-by-step explanation:
Forming quadratic equation and solving:Let the two consecutive odd numbers be (2x + 1) and (2x + 3)
Their product = 35
(2x + 1)(2x + 3) = 35
Use FOIL method.
2x*2x + 2x*3 + 1*2x + 1*3 = 35
4x² + 6x + 2x + 3 = 35
Combine like terms
4x² + 8x + 3 = 35
4x² + 8x + 3 - 35 = 0
4x² + 8x - 32 = 0
Quadratic equation: 4x² + 8x - 32 = 0Solving:
4x² + 8x - 32 = 0
Divide the entire equation by 2
[tex]\sf \dfrac{4}{2}x^2 +\dfrac{8}{2}x - \dfrac{32}{2}=0[/tex]
2x² + 4x - 16 = 0
Sum = 4
Product = -32
Factors = 8 , (-4)
When we multiply 8*(-4) = -32 and when we add 8 + (-4) = 4.
Rewrite the middle term
2x² + 8x - 4x - 16 = 0
2x(x + 4) - 4(x + 4) = 0
(x + 4) (2x - 4) = 0
2x - 4 = 0 {Ignore x +4 = 0 as it gives negative number}
2x = 4
x = 4/2
x= 2
2x + 1 = 2*2 + 1 = 5
2x + 3 = 2*2 +3 = 7
The numbers are 5 , 7
The grade 10 class is going to bake muffins. The recipe that they are going to use requires the following ingredients: RECIPE ✓2 Egga ✔125ml Cooking oll ✓375ml brown sugar (300g) ✓800ml Milk ✓300g Whole wheat flour ✓ 375ml cake flour (210g) ✓5ml Salt ✓ 5ml Vanilla Essence ✓ 10ml Bicarbonate of soda ✓ 250ml Raisins (150g) 2.1 The volume of 150g of Whole wheat is 250ml. Calculate the volume of the Whole wheat flour in the recipe 2.2 When they are all mixed together, all the above ingredients make up 2 litres of mixture (because some parts dissolve into other parts). 2.2.1 Convert 2 litres into ml 2.2.2 How many muffins can the above recipe make if 60ml is required for each muffin? 2.2.3 Using your answer to question 2.2.2, how many eggs will the girls need to buy to make 500 muffins? 2.3 The students need to make 500 muffins, using muffin trays that hold 6 muffins par tray. They plan to put 4 trays at a time into the ovens. Each oven takes 30 minutes to bake. How long will they take to make 500 muffins if they will be using 4 ovens?
The conversion of 2 liters into millimeters from the information regarding the muffins is 2000ml.
How to convert?From the information, we are told to convert 2 litres into ml. This will be:
= 1000 × 2
= 2000ml
The number of eggs that will be bought to make 500 muffins will be:
= 500 × 2
= 1000 eggs.
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help me on this asap
Answer:
A
Explanation:
Formula for the volume of a cone :Volume (cone) = 1/3πr²h
=========================================================
Given :
⇒ r = 4 units
⇒ h = 21 units
=========================================================
Solving :
⇒ Volume (cone) = 1/3 × π x 4² × 21
⇒ Volume (cone) = 16 × 7 × π
⇒ Volume (cone) = 112π units²
-9x²(x²+2x²y - 3y²)
Simplify
−9x^4−18x^4y+27x^2y^2
HAVE A NICE DAY!Answer:
=−18x^4y−9x^4+27x^2y^2
Step-by-step explanation:
(−9x^2)(x^2+2x^2y−3y^2)
=(−9x^2)(x^2+2x^2y+−3y^2)
=(−9x^2)(x^2)+(−9x^2)(2x^2y)+(−9x^2)(−3y^2)
=−9x^4−18x^4y+27x^2y^2
=−18x^4y−9x^4+27x^2y^2
---
Hope I helped! Have a great day :)
solve
16x+8>=12x+20
A. x<=3
B. x<=7
C. x>=3
D. x>=7
Answer: C
Step-by-step explanation:
[tex]16x+8 \geq 12x+20\\ \\ 4x+8 \geq 20\\ \\ 4x \geq 12\\ \\ \boxed{x \geq 3}[/tex]
For the given fact below, which subsequent true/false statement is true?
Fact: Mel received a C+ in Chemistry.
Mel did pass the class , Option B is the correct answer.
The missing options are
Mel does not like chemistry
Mel did pass the class
Mel did not achieve a passing grade for the class
Mel took math this semester
What are True/False Statements ?The statements that are based on fact and is assertive is a true statement and opposite of that is a false statement.
In the question it is mentioned that Mel received a C+ in Chemistry.
It is not known that she took maths test , she did achieve passing grades and by grades it cannot be said if she didn't like chemistry
This can make only Option B statement true , as she did pass the class.
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the lenghts of five boxes are shown in the table which line plot shows the data from the table
Answer:
The bottom right line plot.
Step-by-step explanation:
In the table, 9 1/4 shows up twice. This can be represented in the line plot by putting 2 x's over the 9 1/4 point.
Keiko surveyed people with cell phones. Ages in years = a Texts they send per day = t He drew a best-fit line and determined its equation. Evaluate how many texts a 15 year old would send each day according to Keiko's trend line.
Answer:
68 texts per day
Step-by-step explanation:
The description of the variables in the equation tells you that you want to find t (texts sent per day) for the given value of 'a' (age in years).
__
Substitute the number (15) for the variable (a) and do the arithmetic:
t = -1.63a +92.14
t = -1.63(15) +92.14 = -24.45 +92.14
t = 67.69
Keiko's trend line estimates a 15-year-old would send about 68 texts per day.
The length of a rectangle is 3m less than double the width, and the area of the rectangle is 65m^2 .
What is the length & width of the rectangle?
By solving a quadratic equation, we will see that the length is 10m and the width is 6.5m
How to find the length and width of the rectangle?For a rectangle of width W and length L, the area is:
A = W*L
In this case, we know that the area is 65m² and that the length is 3 meters less than 2 times the width, so:
L = 2*W - 3m
Then we can write:
65m² = (2*W - 3m)*W = 2*W² - 3m*W
This is a quadratic equation:
2*W² - 3m*W - 65m² = 0.
The solutions are given by the Bhaskara's formula:
[tex]W = \frac{3 \pm \sqrt{(-3)^2 - 4*2*(-65)} }{2*2} \\\\W = \frac{3 \pm 23 }{4}[/tex]
We only care for the positive solution, which is:
W = (3m + 23m)/4 = 26m/4 = 6.5m
Then the length is:
L = 2*6.5m - 3m = 10m
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