The number of each type of coin that Joan has are; 16 dimes and 3 quarters
How to convert currencies?
We are told that Joan has a total of 19 coins.
Now, the worth of the coins is $2.35
Let dimes be d and let quarters be q. Thus;
10d + 25q = 235
d + q = 19
Substitute d = 19 - q in the 1st equation to get;
10(19 - q) + 25q = 235
190 - 10q + 25q = 235
15q = 45
q = 45/15
q = 3
Thus;
d = 19 - 3
d = 16
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A class of 30 students plans to collect at least $500 in donations for a rehabilitation camp. They have collected $270. How much more should each student collect?
Which of the following rules is the composition of a dilation of scale factor 2, then a translation of three units to the right? a) (2x+3,y) b) (2x+6, 2y) c) (2x +3, 2y) d) (2x+6, y)
Answer:
The answer is C: (2x +3, 2y)
Step-by-step explanation:
When applying the dilation of a scale factor of 2, you have to apply it to both the x and y coordinate, which means you are multiplying the coordinates by 2.
Let's assume the coordinates you start with are (x, y). Apply the dilation of 2.
(x, y) -----> (2x, 2y)
Now you are moving the figure right. When moving right, this only effects the x coordinate since the x axis moves left and right. Moving right indicates you will add the number of units translated to the x coordinate.
Translation 2 units right:
(2x, 2y) -----> (2x +3, 2y)
The average Wealth of a person in Richville is $150,000 and the average wealth of a
person in Poorville 15 $20,000. Suppose Richville and Poorville combine to form Mediumville.
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
Today only a table is being sold for $364.89. This is 38% of its regular price. What was the price yesterday
Answer:
$960.24
Step-by-step explanation:
Hello!
Let the regular price be x.
38% of x = 0.38x
0.38x = 364.89
Solve for x0.38x = 364.89x = 364.89/0.38x = 960.2368421053 ≈ 960.24The price of the table yesterday was around $960.24.
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.
y=-3³ +4
step by step of the rules and formula of this equation
ZA=C
Round your answer to the nearest hundredth.
C
B
6
8
A
?
Answer:
? = 41.41°
Step-by-step explanation:
The known side length is adjacent to the angle we need to find hence we will use cosine
cosx = adjacent /hypotenuse
cos(?) = 6 / 8
simplify fraction, cos(?) = 3 / 4
? = arccos(3 / 4)
This means that 0.3 is a (n)
number. Rational or irrational
0.3 is a Rational Number written in Decimal Form
0.3 is neither an Integer nor a Whole number.
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.
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]
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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Find the solution set for |2x-3|=9
Answer:
x = 6, -3
Step-by-step explanation:
. . . . . . . . . . . . . . . . .
I will give you brainlest if you are the first one to answer(and the best)
Answer:
4 kg
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
Add to find total mass:
2.5 + 3.5 + 3.5 + 5 + 5.5 = 20
Since there is a total of 5 bags and want to evenly distribute divided by 5,
20 / 5 = 4
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
(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]
A school wants 2 chaperones for every 25 students on a field trip. There are 100 students going on the field trip. How many chaperones does the school need?
A
4
B
8
C
108
D
50
Using proportions, it is found that the number of chaperones that the school needs is given by:
B. 8.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, 2 chaperones are needed for every 25 students. How many are needed for 100 students? The rule of three is given by:
2 chaperones - 25 students
n chaperones - 100 students
Applying cross multiplication:
25n = 2 x 100
n = 200/25
n = 8.
Hence option B is correct.
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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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Find the greatest common factor of 6m² and 7m².
Answer:
your answer is 4 my friend
Step-by-step explanation:
The shorter leg of a right triangle is 5 inches shorter than the longer leg. The hypotenuse is 5 inches longer than the longer leg. Find the side lengths of the triangle.
Answer:
longer leg: 20 in
shorter leg: 15 in
hypotenuse: 25 in
Formulas:
Pythagorean Theorem
[tex]c^2 = a^2 + b^2[/tex]
c ... hypotenuse
a ... one leg
b ... another leg
Pythagorean theorem is used in right triangles (triangles in which one angle is 90°).
Step-by-step explanation:
longer leg: x
shorter leg: x - 5
hypotenuse: x + 5
To find x (longer leg), let's use Pythagorean theorem.
[tex]c^2 = a^2 + b^2\\(x+5)^2 = x^2 + (x-5)^2\\x^2 + 10x + 25= x^2 + x^2 -10x + 25\\x^2 + 10x = 2x^2 - 10x\\0 = x^2 - 20x[/tex]
Now let's factorize to get solutions for x.
[tex]0 = x(x-20)[/tex]
First solution:
[tex]x = 0[/tex]
Second solution:
[tex]x - 20 = 0\\x = 20[/tex]
Since a side of a triangle has to be a positive number, x is equal to 20.
Now let's just substitute x back to get side lengths. From the question the lengths are in inches.
longer leg: x = 20 in
shorter leg: x - 5 = 20 - 5 = 15 in
hypotenuse: x + 5 = 20 + 5 = 25 in
7) $72.45 -28.98 Rounded estimate
Answer:
$43
Step-by-step explanation:
$72.45 can be rounded down to $72.00
$28.98 can be rounded up to $29.00
$72-$29= $43
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.
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]
Which shows one way to determine the factors of Which shows one way to determine the factors of x3 + 4x2 + 5x + 20 by grouping? by grouping?
The factored expression of the expression x^3 + 4x^2 +5x + 20 is (x^2 + 5)(x + 4)
How to determine the factors?The expression is given as:
x^3 + 4x^2 +5x + 20
Group the expression into two
(x^3 + 4x^2) + (5x + 20)
Factorize each group
x^2(x + 4) + 5(x + 4)
Factor out x + 4
(x^2 + 5)(x + 4)
Hence, the factored expression of the expression x^3 + 4x^2 +5x + 20 is (x^2 + 5)(x + 4)
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can you help me with this question
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]
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
Homework Due Tomorrow please help me it would be great
Answer:
c
Step-by-step explanation:
work out the average for the data below
Which function is shown in the graph below?
O y = logo 4x
O y = log₁x
O y = log3x
O y = log10x
The correct function shown in the graph is,
⇒ log₁₀ (ax) = 1
What is mean by Function?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).
It has been given that the point (3,1) is on the graph. For the point (3,1) to be on the graph, the following must hold true:
⇒ log₁₀ (ax) = 1
or , ax = 10¹ = 10
Thus, x = 10/a
So, in order for the point (3,1) to lie on the graph, of all the given options the closest we can get is when we have Option D, that is, when a = 3. That will make x = 3.33 and thus, .
⇒ log (3 × 3.33) = 0.99 ≈ 1
Thus, out of the given options only Option D seems to be the most probable answer.
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A leak in a pool causes the height of the water to decrease by 0.25 foot over 2 hours. After the leak is fixed, the height of the water is 4.75 feet. The equation 4.75 = x + (negative 0.25) can be used to find x, the original height of the water in a pool.
What was the original height of the water in the pool in feet?
4.5
5.0
6.5
7.0
The original height of the water in a pool is 5 ft , Option B is the correct answer.
What is an Equation ?An equation can be defined as a mathematical statement when two algebraic expressions are equated using an equal sign.
It is given in the question that
A leak in a pool causes the height of the water to decrease by 0.25 foot over 2 hours.
the height of the water is 4.75 feet.
The equation
4.75 = x + (negative 0.25)
can be used to find x, the original height of the water in a pool.
4.75 = x - 0.25
x = 5
Therefore the original height of the water in a pool is 5 ft , Option B is the correct answer.
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Answer:
B
Step-by-step explanation: