20. The table below shows the ages of children in a cricket camp.
\begin{tabular}{|c|c|}
\hline Age & Number of Children \\
\hline 9 & 12 \\
\hline 8 & 15 \\
\hline 7 & 22 \\
\hline 6 & 13 \\
\hline
\end{tabular} How many children are under the age of 8 ? Answer children
Simplify the following expression by combining like terms.
85x5+14x2+41x5−17x2−1985x5+14x2+41x5−17x2−19=□
(Use integers or fractions for any numbers in the expression.)
Part 1 of 3 Use a table to find the product of (3x+4)(x2+3x−2). How are the like terms in a table arranged? Complete the table below.
\begin{tabular}{|c|c|c|c|}
\hline & x2 & +3x & -2 \\
\hline 3x & □ & □ & □ \\
\hline+4 & □ & □ & □ \\
\hline
\end{tabular}
(Simplify your answers.)
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Evaluate each expression if a=87,b=−167,c=0.8,d=41. (Example 1) 1. ba−c+d−2051 2. a+b+cd=8051 3. c−a+db 4. ab+dc 5. a2−b 6. a+cb−d Evaluate each expression if a=107,b=53,c=−1.9. and d=−21. Write vour answer in
1 Exercice 1 : Factorisation sans identité remarquable Factoriser les expressions suivantes
a. 16x+4x(2x+3)
b. (2x+1)(4x+3)−(2x+1)
c. (5x+3)(2x−1)+4x(5x+3)
d. (3x+1)3+(3x+1)(4x+2)+4(3x+1)
g) Of the $500000 paid for the property, $150000 was for the block of land, and the rest was for building the house. Find the ratio of land to total property price.
) 菨) An ice cream shop in Kingwood sells a variety of different flavors and keeps track of its weekly sales. Ice cream sales
(1) 㸚, Simplify your answer.
Find the sum of the pair of complex numbers. Then graph both complex numbers and their resultant.
5−6i,−2+4i The sum is □
(Type your answer in the form a+bi.)
The Motor Vehicle Department has found that the probability of a person passing the test for a driver's license on the first try is 0.75 . The probability that an individual who fails on the first test will pass on the second try is 0.82 , and the probability that an individual who fails the first and second tests will pass the third time is 0.68 . Find the probabilities that an individual will do the following.
a. P(Fail both the first and second tests)
b. P(Fail three times in a row)
c. P (Require at least two tries)
a. P (fails both the first and second tests) =□
(Type an integer or decimal rounded to four decimal places as needed.)
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9 Express each of the following as a simplified rate.
a 180 students on 3 buses
b $5.60 for 4 kg
c 186 km in 221 hours
5:2 10 Find the average rate for each situation.
a Thelma drove 8000 km in 50 days
b Callum saved $1250 in 6 months
c. Ainslie grew 20 cm in 221 years 11 Who earns the most, and by how much, if Kelly is paid $96570 a year and Todd earns $7985 each month? Which is faster 70km/h or 21m/s ?
Calculate the distance between the points F=(−4,4) and G=(−1,9) in the coordinate plane.
Give an exact answer (not a decimal approximation). Distance: □
A bag contains fourteen marbles of assorted colors, of which just one is red. Use the symbol C(n,r) to answer questions (a) through (e).
(a) In how many ways can a subset of any six marbles be chosen?
C(14,6)
(b) In how many ways can a subset of six marbles be chosen, none red?
C(13,6)
(c) In how many ways can a subset of six marbles be chosen, including the red marble?
C(□ , , ,
A Dag contains fourteen marbles of assorted colors, of which just one is red. Use the symbol C(n,r) to answer questions (a) through (e).
C(14,6)
(b) In how many ways can a subset of six marbles be chosen, none red?
C(13,6)
(c) In how many ways can a subset of six marbles be chosen, including the red marble?
C(13,5)
(d) What formula expresses the fact that your answer to part (a) is the sum of your answers to parts (b) and (c)?
A. C(14,6)=C(13,6)+C(13,5)
B. C(14,5)=C(14,6)+C(13,6)
C. C(13,5)=C(14,5)+C(14,6)
D. C(13,6)=C(13,5)+C(14,5)
(e) Create a "marble story" to derive the formula C(8,5)=C(7,5)+C(7,4). Complete the story below. A bag has □ marbles of assorted colors, of which □ is blue. Choosing a subset of any □ marbles is the same as choosing a subset of □ marbles with none blue □ choosing a subset of □ marbles with one blue.
Write log6150 in terms of natural logarithms using the change-of-base theorem. The expression log6150 in terms of natural logarithms is written as □
(Do not evaluate. Do not simplify.)
ven this expression to simplify.
(x+1)−3(x+3)
steps in simplifying:
(−2)(1)+−3(x)+(−3)(3)+−3x+−9 Which statements are true about the steps An used? Check all that apply.
In step 1, she distributed -2 through the parentheses.
In step 1, she distributed 3 through the parentheses.
thystep 2, she added the factor to the value the parentheses.
1. The following data was obtained when magnesium oxide was produced from the following reaction
2Mg+O2→2MgO Table 1: Masses of reactants and products
\begin{tabular}{|l|l|}
\hline Mass of Test Tube & 22.42 g \\
\hline Mass of Test Tube and Magnesium & 22.52 g \\
\hline Mass of Test Tube and Product & 23.01 g \\
\hline
\end{tabular}
a) Calculate the mass of magnesium reacted. 0.19
b) Calculate the mass of magnesium oxide produced. 0.59 g
c) Calculate the mass of oxygen gas reacted. 0.49 g
d) Calculate the experimental percent composition of magnesium and oxygen in magnesium oxide. 16.9%−%Mg;83.1%0=7.0
e) What is the theoretical percent of magnesium in magnesium
(HINT: this is the value for the percent composition using the %Mg=60.3%;20:39.7%. 2. Calculate the molar mass of eqch of the following:
a) Zinc chloride 136.28g/mol
b) Sodium phosphate 163.94g/mol 3. What is the mass of 2.36 moles of silver nitrate?
401g 4. How many moles are in 5.62×1027 molecules of sodium chloride? 9.34×103 moles. 5. How many molecules are in a 3.54 g sample of propane (C3H8) ? How many atoms are in this sample? 4.83×1022 6. An inorganic salt is composed of 38.8% calcium, 20.0% phosphorus, and 41.2% oxygen. What is the empirical formula for this salt? Ca3P2O8 7. The empirical formula of a certain chemical is C6H2OCl2. If the molar mass is 322g/mol, what is its molecular formula? C12H4O2Cl4
Simplify the algebraic expression by combining like terms. YOUR ANSWER MUST BE IN ALPHABETICAL ORDER WITH THE CONSTANT AT THE END. NO SPACES
12p−p−p−p−p=□
Answer each part. If necessary, round your answers to the nearest hundredth.
(a) Hong runs 7 miles in 38 minutes. How many minutes does he take per mile?
In the following problem, divide using long division. State the quotient, q(x), and the remainder, r(x).
x−44x4−3x2+4xx−44x4−3x2+4x=□+x−4□
(Simplify your answers. Do not factor. Use integers or fractions for any numbers in the expressions.)
Find the perimeter of the rectangle. Express the perimeter using the same unit of measure that appears on the given sides. The perimeter of the rectangle is □□
5. Jeremy operates a driving school. Last year, he earned $44651.00. He spent $14236.00 on business expenses.
a) What was Jeremy's net income?
b) A hybrid car would run on electricity as well as gasoline. How could using a hybrid car increase Jeremy's profit?
c) Do you agree that buying a hybrid car would help Jeremy's profit? Explain.
d) What are some other ways that a driving school could increase its profit?
What rotation must the driver gear make for gear A to rotate 90∘ clockwise? Explain how you found your answer. If gear A rotates 90∘, then it turns through □ teeth on the gear. This corresponds to □ teeth on the driver gear, which has 16 teeth in total. So, the driver gear must make a rotation of □□ (Type whole numbers.)